mages' blog

We are delighted to announce that the programme for the 4th R in Insurance conference at Cass Business School in London, 11 July 2016, have been finalised.

Register by the end of May to get the early bird booking fee.

The organisers gratefully acknowledge the sponsorship of Verisk, Mirai Solutions, Applied AI, Studio, CYBAEA and Oasis, without whom the event wouldn't be possible.

I had the great pleasure time to attend the Warsaw R meetup last Thursday. The organisers Olga Mierzwa and Przemyslaw Biecek had put together an event with a focus on R in Insurance (btw, there is a conference with the same name), discussing examples of pricing and reserving in general and life insurance.

Experience vs. Data

I kicked off with some observations of the challenges in insurance pricing. Accidents are thankfully rare events, that's why we buy insurance. Hence, there is often not a lot of claims data available for pricing. Combining the information from historical data and experts with domain knowledge can provide a rich basis for the assessment of risk. I presented some examples using Bayesian analysis to understand the probability of an event occurring. Regular readers of my blog will recognise the examples from earlier posts. You find my slides on GitHub.

Download slides

Non-life insurance in R

Emilia Kalarus from Triple A shared some of her experience of using R in non-life insurance companies. She focused on the challenges in working across teams, with different systems, data sets and mentalities.

As an example, Emilia talked about the claims reserving process, which in her view should be embedded in the full life cycle of insurance, namely product development, claims, risk and performance management. Following this thought, she presented an idea for claims reserving that models the life of a claim from not incurred and not reported (NINR), to incurred but not reported (IBNR), reported but not settled (RBNS) and finally paid.

Stochastic mortality modelling

The final talk was given by Adam Wróbel from the life insurer Nationale Nederlanden, discussing stochastic mortality modelling. Adam's talk on analysing mortality made me realise that life and non-life insurance companies may be much closer to each other than I thought.

Although life and non-life companies are usually separated for regulatory reasons, they both share the fundamental challenge of predicting future cash flows. An example where the two industries meet is product liability.

Over the last century, technology has changed our environment fundamentally, more so than ever before. Yet, we still don't know which long-term impact some of the new technologies and products will have on our life expectancy. Some will prolong our lives, others may make us ill.

A classic example is asbestos, initial regarded as a miracle mineral, as it was impossible to set on fire, abundant, cheap to mine, and easy to manufacture. Not surprisingly it was widely used until it was linked to causing cancer. Over the last 35 years, the non-life insurance industry has paid well in excess of hundred billion dollars in compensations.

Slides and Code

The slides and R code of the presentations are hosted on the Warsaw R GitHub page.

I continue with the growth curve model for loss reserving from last week's post. Today, following the ideas of James Guszcza [2] I will add an hierarchical component to the model, by treating the ultimate loss cost of an accident year as a random effect. Initially, I will use the nlme R package, just as James did in his paper, and then move on to Stan/RStan [6], which will allow me to estimate the full distribution of future claims payments.

Last week's model assumed that cumulative claims payment could be described by a growth curve. I used the Weibull curve and will do so here again, but others should be considered as well, e.g. the log-logistic cumulative distribution function for long tail business, see [1].
The growth curve describes the proportion of claims paid up to a given development period compared to the ultimate claims cost at the end of time, hence often called development pattern. Cumulative distribution functions are often considered, as they increase monotonously from 0 to 100%. Multiplying the development pattern with the expected ultimate loss cost gives me then the expected cumulative paid to date value.

However, what I'd like to do is the opposite, I know the cumulative claims position to date and wish to estimate the ultimate claims cost instead. If the claims process is fairly stable over the years and say, once a claim has been notified the payment process is quite similar from year to year and claim to claim, then a growth curve model is not unreasonable. Yet, the number and the size of the yearly claims will be random, e.g. if a windstorm, fire, etc occurs or not. Hence, a random effect for the ultimate loss cost across accident years sounds very convincing to me.

Here is James' model as described in [2]:
\[
\begin{align}
CL_{AY, dev} & \sim \mathcal{N}(\mu_{AY, dev}, \sigma^2_{dev}) \\
\mu_{AY,dev} & = Ult_{AY} \cdot G(dev|\omega, \theta)\\
\sigma_{dev} & = \sigma \sqrt{\mu_{dev}}\\
Ult_{AY} & \sim \mathcal{N}(\mu_{ult}, \sigma^2_{ult})\\
G(dev|\omega, \theta) & = 1 - \exp\left(-\left(\frac{dev}{\theta}\right)^\omega\right)
\end{align}
\]The cumulative losses \(CL_{AY, dev}\) for a given accident year \(AY\) and development period \(dev\) follow a Normal distribution with parameters \(\mu_{AY, dev}\) and \(\sigma_{dev}\).

The mean itself is modelled as the product of an accident year specific ultimate loss cost \(Ult_{AY}\) and a development period specific parametric growth curve \(G(dev | \omega, \theta)\). The variance is believed to increase in proportion with the mean. Finally, the ultimate loss cost is modelled with a Normal distribution as well.

Assuming a Gaussian distribution of losses doesn't sound quite intuitive to me, as loss are often skewed to the right, but I shall continue with this assumption here to make a comparison with [2] possible.

Using the example data set given in the paper I can reproduce the result in R with nlme:

The fit looks pretty good, with only 5 parameters. See James' paper for a more detailed discussion.

Let's move this model into Stan. Here is my attempt, which builds on last week's pooled model. With the generated quantities code block I go beyond the scope of the original paper, as I try to estimate the full posterior predictive distribution as well.
The 'trick' is the line mu[i] <- ult[origin[i]] * weibull_cdf(dev[i], omega, theta); where I have an accident year (here labelled origin) specific ultimate loss.

The notation ult[origin[i]] illustrates the hierarchical nature in Stan's language nicely.

Let's run the model:
The estimated parameters look very similar to the nlme output above.

Let's take a look at the parameter traceplot and the densities of the estimated ultimate loss costs by origin year.
This looks all not too bad. The trace plots don't show any particular patterns, apart from \(\sigma_{ult}\), which shows a little skewness.

The generated quantities code block in Stan allows me to get also the predictive distribution beyond the current data range. Here I forecast claims up to development year 12 and plot the predictions, including the 95% credibility interval of the posterior predictive distribution with the observations.

The model seems to work rather well, even with the Gaussian distribution assumptions. Yet, it has still only 5 parameters. Note, this model doesn't need an additional artificial tail factor either.

Conclusions

The Bayesian approach sounds to me a lot more natural than many classical techniques around the chain-ladder methods. Thanks to Stan, I can get the full posterior distributions on both, the parameters and predictive distribution. I find communicating credibility intervals much easier than talking about the parameter, process and mean squared error.

James Guszcza contributed to a follow-up paper with Y. Zhank and V. Dukic [3] that extends the model described in [2]. It deals with skewness in loss data sets and the autoregressive nature of the errors in a cumulative time series.

Frank Schmid offers a more complex Bayesian analysis of claims reserving in [4], while Jake Morris highlights the similarities between a compartmental model used in drug research and loss reserving [5].

Finally, Glenn Meyers published a monograph on Stochastic Loss Reserving Using Bayesian MCMC Models earlier this year [7] that is worth taking a look at.

References

[1] David R. Clark. LDF Curve-Fitting and Stochastic Reserving: A Maximum Likelihood Approach. Casualty Actuarial Society, 2003. CAS Fall Forum.

[2] James Guszcza. Hierarchical Growth Curve Models for Loss Reserving, 2008, CAS Fall Forum, pp. 146–173.

[3] Y. Zhang, V. Dukic, and James Guszcza. A Bayesian non-linear model for forecasting insurance loss payments. 2012. Journal of the Royal Statistical Society: Series A (Statistics in Society), 175: 637–656. doi: 10.1111/j.1467-985X.2011.01002.x

[4] Frank A. Schmid. Robust Loss Development Using MCMC. Available at SSRN. See also http://lossdev.r-forge.r-project.org/

[5] Jake Morris. Compartmental reserving in R. 2015. R in Insurance Conference.

[6] Stan Development Team. Stan: A C++ Library for Probability and Sampling, Version 2.8.0. 2015. http://mc-stan.org/.

[7] Glenn Meyers. Stochastic Loss Reserving Using Bayesian MCMC Models. Issue 1 of CAS Monograph Series. 2015.

Session Info

R version 3.2.2 (2015-08-14)
Platform: x86_64-apple-darwin13.4.0 (64-bit)
Running under: OS X 10.11.1 (El Capitan)

locale:
[1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8

attached base packages:
[1] stats  graphics  grDevices utils datasets  methods   base     

other attached packages:
[1] ChainLadder_0.2.3 rstan_2.8.0   ggplot2_1.0.1  Rcpp_0.12.1      
[5] lattice_0.20-33  

loaded via a namespace (and not attached):
 [1] nloptr_1.0.4       plyr_1.8.3         tools_3.2.2       
 [4] digest_0.6.8       lme4_1.1-10        statmod_1.4.21    
 [7] gtable_0.1.2       nlme_3.1-122       mgcv_1.8-8        
[10] Matrix_1.2-2       parallel_3.2.2     biglm_0.9-1       
[13] SparseM_1.7        proto_0.3-10       coda_0.18-1       
[16] gridExtra_2.0.0    stringr_1.0.0      MatrixModels_0.4-1
[19] lmtest_0.9-34      stats4_3.2.2       grid_3.2.2        
[22] nnet_7.3-11        tweedie_2.2.1      inline_0.3.14     
[25] cplm_0.7-4         minqa_1.2.4        actuar_1.1-10     
[28] reshape2_1.4.1     car_2.1-0          magrittr_1.5      
[31] scales_0.3.0       codetools_0.2-14   MASS_7.3-44       
[34] splines_3.2.2      rsconnect_0.3.79   systemfit_1.1-18  
[37] pbkrtest_0.4-2     colorspace_1.2-6   quantreg_5.19     
[40] labeling_0.3       sandwich_2.3-4     stringi_1.0-1     
[43] munsell_0.4.2      zoo_1.7-12

Last week I posted a biological example of fitting a non-linear growth curve with Stan/RStan. Today, I want to apply a similar approach to insurance data using ideas by David Clark [1] and James Guszcza [2].

Instead of predicting the growth of dugongs (sea cows), I would like to predict the growth of cumulative insurance loss payments over time, originated from different origin years. Loss payments of younger accident years are just like a new generation of dugongs, they will be small in size initially, grow as they get older, until the losses are fully settled.

Here is my example data set:

Following the articles cited above I will assume that the growth can be explained by a Weibull curve, with two parameters \(\theta\) (scale) and \(\omega\) (shape):
\[
G(dev|\omega, \theta) = 1 - \exp\left(-\left(\frac{dev}{\theta}\right)^\omega\right)
\]Inspired by the classical over-dispersed Poisson GLM in actuarial science, Guszcza [2] assumes a power variance structure for the process error as well. For the purpose of this post I will assume that claims cost follow a Normal distribution, to make a comparison with a the classical least square regression easier. With a prior estimate of the ultimate claims cost the cumulative loss can be modelled as:
\[
\begin{align}
CL_{AY, dev} & \sim \mathcal{N}(\mu_{dev}, \sigma^2_{dev}) \\
\mu_{dev} & = Ult \cdot G(dev|\omega, \theta)\\
\sigma_{dev} & = \sigma \sqrt{\mu_{dev}}
\end{align}
\]Perhaps, the above formula suggests a hierarchical modelling approach, with different ultimate loss costs by accident year. Indeed, this is the focus of [2] and I will endeavour to reproduce the results with Stan in my next post, but today I will stick to a pooled model that assumes a constant ultimate loss across all accident years, i.e. \(Ult_{AY} = Ult \;\forall\; AY\).

To prepare my analysis I read in the data as a long data frame instead of the matrix structure above. Additionally, I compose another data frame that I will use later to predict payments two years beyond the first 10 years. Furthermore, to align the output with [2] I relabelled the development periods from years to months, so that year 1 becomes month 6, year 2 becomes month 18, etc. The accident years run from 1991 to 2000, while the variable origin maps those years from 1 to 10.

To get a reference point for Stan I start with a non-linear least square regression:

The output above doesn't look unreasonable, apart from the accident years 1991, 1992 and 1998. The output of gnls gives me an opportunity to provide my prior distributions with good starting points. I will use an inverse Gamma as a prior for \(\sigma\), constrained Normals for the parameters \(\theta, \omega\) and \(Ult\) as well. If you have better ideas, then please get in touch.

The Stan code below is very similar to last week. Again, I am interested here in the posterior distributions, hence I add a block to generate quantities from those. Note, Stan comes with a build-in function for the cumulative Weibull distribution weibull_cdf.

I store the Stan code in a separate text file, which I read into R to compile the model. The compilation takes a little time. The sampling itself is done in a few seconds.

Let's take a look at the output:

The parameters are a little different to the output of gnls, but well within the standard error. From the plots I notice that the samples for the ultimate loss as well as for \(\theta\) are a little skewed to the right. Well, assuming cumulative losses to follow a Normal distribution was a bit a of stretch to start with. Still, the samples seem to converge.

Finally, I can plot the 90% credible intervals of the posterior distributions.

The 90% prediction credible interval captures most of the data and although this model might not be suitable for reserving individual accident years, it could provide an initial starting point for further investigations. Additionally, thanks to the Bayesian model I have access to the full distribution, not just point estimators and standard errors.

My next post will continue with this data set and the ideas of James Guszcza by allowing the ultimate loss cost to vary by accident year, treating it as a random effect. Here is a teaser of what the output will look like:

References

[1] David R. Clark. LDF Curve-Fitting and Stochastic Reserving: A Maximum Likelihood Approach. Casualty Actuarial Society, 2003. CAS Fall Forum.

[2] Guszcza, J. Hierarchical Growth Curve Models for Loss Reserving, 2008, CAS Fall Forum,
pp. 146–173.

Session Info

R version 3.2.2 (2015-08-14)
Platform: x86_64-apple-darwin13.4.0 (64-bit)
Running under: OS X 10.11.1 (El Capitan)

locale:
[1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods  
[7] base     

other attached packages:
[1] rstan_2.8.0    ggplot2_1.0.1     Rcpp_0.12.1      
[4] nlme_3.1-122   lattice_0.20-33   ChainLadder_0.2.3

loaded via a namespace (and not attached):
 [1] nloptr_1.0.4       plyr_1.8.3         tools_3.2.2       
 [4] digest_0.6.8       lme4_1.1-10        statmod_1.4.21    
 [7] gtable_0.1.2       mgcv_1.8-8         Matrix_1.2-2      
[10] parallel_3.2.2     biglm_0.9-1        SparseM_1.7       
[13] proto_0.3-10       gridExtra_2.0.0    coda_0.18-1       
[16] stringr_1.0.0      MatrixModels_0.4-1 stats4_3.2.2      
[19] lmtest_0.9-34      grid_3.2.2         nnet_7.3-11       
[22] inline_0.3.14      tweedie_2.2.1      cplm_0.7-4        
[25] minqa_1.2.4        reshape2_1.4.1     car_2.1-0         
[28] actuar_1.1-10      magrittr_1.5       codetools_0.2-14  
[31] scales_0.3.0       MASS_7.3-44        splines_3.2.2     
[34] systemfit_1.1-18   rsconnect_0.3.79   pbkrtest_0.4-2    
[37] colorspace_1.2-6   labeling_0.3       quantreg_5.19     
[40] sandwich_2.3-4     stringi_1.0-1      munsell_0.4.2     
[43] zoo_1.7-12

Following the successful 3rd R in Insurance conference in Amsterdam this year, we will return to London next year. We will be back at Cass Business School, 11 July 2016.

The event will focus again on the use of R in insurance, bringing together experts from industry and academia with a diverse background of disciplines, such as actuarial science, catastrophe modelling, finance, statistics and computer science.

We are delighted to announce or keynote speakers already: Dan Murphy and Mario V. Wüthrich.

More details about the event will be published in due course here. For now, save the date in your diary.

PS: The picture above is a cluster analysis of the Lloyd's building in R.

We released version 0.2.2 of ChainLadder a few weeks ago. This version adds back the functionality to estimate the index parameter for the compound Poisson model in glmReserve using the cplm package by Wayne Zhang.

Ok, what does this all mean? I will run through a couple of examples and look behind the scene of glmReserve. However, the clue is in the title, glmReserve is a function that uses a generalised linear model to estimate future claims, assuming claims follow a Tweedie distribution. I should actually talk about a family of distributions that is known as Tweedie, named by Bent Jørgensen after Maurice Tweedie. Joe Rickert published a nice post about the Tweedie distribution last year.

Like most other functions in ChainLadder, glmReserve purpose is to predict future insurance claims based on historical data.

The data at hand is often presented in form of a claims triangle, such as the following example data set from the ChainLadder package:

library(ChainLadder)
cum2incr(UKMotor) 
##       dev
## origin    1    2    3    4    5   6   7
##   2007 3511 3215 2266 1712 1059 587 340
##   2008 4001 3702 2278 1180  956 629  NA
##   2009 4355 3932 1946 1522 1238  NA  NA
##   2010 4295 3455 2023 1320   NA  NA  NA
##   2011 4150 3747 2320   NA   NA  NA  NA
##   2012 5102 4548   NA   NA   NA  NA  NA
##   2013 6283   NA   NA   NA   NA  NA  NA

The rows present different origin periods in which accidents occurred and the columns along each row show the incremental reported claims over the years (the data itself is stored in a cumulative form).

Suppose all claims will be reported within 7 years, then I'd like to know how much money should be set aside for the origin years 2008 to 2013 for claims that have incurred but not been reported (IBNR) yet. Or, to put it differently, I have to predict the NA fields in the bottom right hand triangle.

First, let's reformat the data as it would be stored in a database, that is in a long format of incremental claims over the years (I add the years also as factors, which I will use later):

claims <- as.data.frame(cum2incr(UKMotor)) # convert into long format
library(data.table)
claims <- data.table(claims)
claims <- claims[ , ':='(cal=origin+dev-1, # calendar period
                         originf=factor(origin),
                         devf=factor(dev))]
claims <- claims[order(dev), cum.value:=cumsum(value), by=origin]
setnames(claims, "value", "inc.value")
head(claims)
##    origin dev inc.value  cal originf devf cum.value
## 1:   2007   1      3511 2007    2007    1      3511
## 2:   2008   1      4001 2008    2008    1      4001
## 3:   2009   1      4355 2009    2009    1      4355
## 4:   2010   1      4295 2010    2010    1      4295
## 5:   2011   1      4150 2011    2011    1      4150
## 6:   2012   1      5102 2012    2012    1      5102

Let's visualise the data:

library(lattice)
xyplot(cum.value/1000 + log(inc.value) ~ dev , groups=origin, data=claims, 
       t="b", par.settings = simpleTheme(pch = 16),
       auto.key = list(space="right",
                       title="Origin\nperiod", cex.title=1,
                       points=FALSE, lines=TRUE, type="b"),
       xlab="Development period", ylab="Amount",
       main="Claims development by origin period",
       scales="free")

The left plot of the chart above shows the cumulative claims payment over time, while the right plot shows the log-transformed incremental claims development for each origin/accident year.

One of the oldest methods to predict future claims development is called chain-ladder, which can be regarded as a weighted linear regression through the origin of cumulative claims over the development periods. Multiplying those development factors to the latest available cumulative position allows me to predict future claims in an iterative fashion.

It is well know in actuarial science that a Poisson GLM produces the same forecasts as the chain-ladder model.

Let's check:

# Poisson model
mdl.pois <- glm(inc.value ~ originf + devf, data=na.omit(claims), 
                family=poisson(link = "log"))
# predict claims
claims <- claims[, ':='(
  pred.inc.value=predict(mdl.pois, 
                         .SD[, list(originf, devf, inc.value)],
                         type="response")), by=list(originf, devf)]
# sum of future payments
claims[cal>max(origin)][, sum(pred.inc.value)]
## [1] 28655.77
# Chain-ladder forecast
summary(MackChainLadder(UKMotor, est.sigma = "Mack"))$Totals[4,]
## [1] 28655.77

Ok, this worked. However, both of these models make actually fairly strong assumptions. The Poisson model by its very nature will only produce whole numbers, and although payments could be regarded as whole numbers, say in pence or cents, it does feel a little odd to me. Similarly, modelling the year on year developments via a weighted linear regression through the origin, as in the case of the chain-ladder model, sounds not intuitive either.

There is another aspect to highlight with the Poisson model; its variance is equal to the mean. Yet, in real data I often observe that the variance increases in proportion to the mean. Well, this can be remedied by using an over-dispersed quasi-Poisson model.

I think a more natural approach would be to assume a compound distribution that models the frequency and severity of claims separately, e.g. Poisson frequency and Gamma severity.

Here the Tweedie distributions comes into play.

Tweedie distributions are a subset of what are called Exponential Dispersion Models. EDMs are two parameter distributions from the linear exponential family that also have a dispersion parameter \(\Phi\).

Furthermore, the variance is a power function of the mean, i.e. \(\mbox{Var}(X)=\Phi \, E[X]^p\).

The canonical link function for a Tweedie distribution in a GLM is the power link \(\mu^q\) with \(q=1-p\). Note, \(q=0\) is interpreted as \(\log(\mu)\).

Thus, let \(\mu_i = E(y_i)\) be the expectation of the ith response. Then I have the following model.
\[
y \sim \mbox{Tweedie}(q, p)\\
E(y) = \mu^q = Xb \\
\mbox{Var}(y) = \Phi \mu^p
\]The variance power \(p\) characterises the distribution of the responses \(y\). The following are some special cases:

• Normal distribution, p = 0
• Poisson distribution, p = 1
• Compound Poisson-Gamma distribution, 1 < p < 2
• Gamma distribution, p = 2
• Inverse-Gaussian, p = 3
• Stable, with support on the positive real numbers, p > 2

Finally, I get back to the glmReserve function, which Wayne Zhang, the other author of the cplm package, contributed to the ChainLadder package.

With glmReserve I can model a claims triangle using the Tweedie distribution family.

In my first example I set use the parameters \(p=1, q=0\), which should return the results of the Poisson model.

(m1 <- glmReserve(UKMotor, var.power = 1, link.power = 0))
##       Latest Dev.To.Date Ultimate  IBNR       S.E         CV
## 2008   12746   0.9732000    13097   351  125.8106 0.35843464
## 2009   12993   0.9260210    14031  1038  205.0826 0.19757473
## 2010   11093   0.8443446    13138  2045  278.8519 0.13635790
## 2011   10217   0.7360951    13880  3663  386.7919 0.10559429
## 2012    9650   0.5739948    16812  7162  605.2741 0.08451188
## 2013    6283   0.3038201    20680 14397 1158.1250 0.08044210
## total  62982   0.6872913    91638 28656 1708.1963 0.05961042

Perfect, I get the same results, plus further information about the model.

Setting the argument var.power=NULL will estimate \(p\) in the interval \((1,2)\) using the cplm package.

(m2 <- glmReserve(UKMotor, var.power=NULL))
##       Latest Dev.To.Date Ultimate  IBNR       S.E         CV
## 2008   12746   0.9732000    13097   351  110.0539 0.31354394
## 2009   12993   0.9260870    14030  1037  176.9361 0.17062307
## 2010   11093   0.8444089    13137  2044  238.5318 0.11669851
## 2011   10217   0.7360951    13880  3663  335.6824 0.09164138
## 2012    9650   0.5739948    16812  7162  543.6472 0.07590718
## 2013    6283   0.3038201    20680 14397 1098.7988 0.07632138
## total  62982   0.6873063    91636 28654 1622.4616 0.05662252
m2$model
## 
## Call:
## cpglm(formula = value ~ factor(origin) + factor(dev), link = link.power, 
##     data = ldaFit, offset = offset)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -6.7901  -1.6969   0.0346   1.6087   8.4465  
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         8.25763    0.04954 166.680  < 2e-16 ***
## factor(origin)2008  0.03098    0.05874   0.527 0.605588    
## factor(origin)2009  0.09999    0.05886   1.699 0.110018    
## factor(origin)2010  0.03413    0.06172   0.553 0.588369    
## factor(origin)2011  0.08933    0.06365   1.403 0.180876    
## factor(origin)2012  0.28091    0.06564   4.279 0.000659 ***
## factor(origin)2013  0.48797    0.07702   6.336 1.34e-05 ***
## factor(dev)2       -0.11740    0.04264  -2.753 0.014790 *  
## factor(dev)3       -0.62829    0.05446 -11.538 7.38e-09 ***
## factor(dev)4       -1.03168    0.06957 -14.830 2.28e-10 ***
## factor(dev)5       -1.31346    0.08857 -14.829 2.28e-10 ***
## factor(dev)6       -1.86307    0.13826 -13.475 8.73e-10 ***
## factor(dev)7       -2.42868    0.25468  -9.536 9.30e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Estimated dispersion parameter: 10.788
## Estimated index parameter: 1.01 
## 
## Residual deviance: 299.27  on 15  degrees of freedom
## AIC:  389.18 
## 
## Number of Fisher Scoring iterations:  4

From the model I note that the dispersion parameter \(\phi\) was estimated as 10.788 and the index parameter \(p\) as 1.01.

Not surprisingly the estimated reserves are similar to the Poisson model, but with a smaller predicted standard error.

Intuitively the modelling approach makes a lot more sense, but I end up with one parameter for each origin and development period, hence there is a danger of over-parametrisation.

Looking at the plots above again I note that many origin periods have a very similar development. Perhaps a hierarchical model would be more appropriate?

For more details on glmReserve see the help file and package vignette.

Session Info

R version 3.2.2 (2015-08-14)
Platform: x86_64-apple-darwin13.4.0 (64-bit)
Running under: OS X 10.10.5 (Yosemite)

locale:
[1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] data.table_1.9.6  ChainLadder_0.2.2

loaded via a namespace (and not attached):
 [1] Rcpp_0.12.1        nloptr_1.0.4       plyr_1.8.3        
 [4] tools_3.2.2        digest_0.6.8       lme4_1.1-9        
 [7] statmod_1.4.21     gtable_0.1.2       nlme_3.1-121      
[10] lattice_0.20-33    mgcv_1.8-7         Matrix_1.2-2      
[13] parallel_3.2.2     biglm_0.9-1        SparseM_1.7       
[16] proto_0.3-10       coda_0.17-1        stringr_1.0.0     
[19] MatrixModels_0.4-1 stats4_3.2.2       lmtest_0.9-34     
[22] grid_3.2.2         nnet_7.3-10        tweedie_2.2.1     
[25] cplm_0.7-4         minqa_1.2.4        ggplot2_1.0.1     
[28] reshape2_1.4.1     car_2.1-0          actuar_1.1-10     
[31] magrittr_1.5       scales_0.3.0       MASS_7.3-44       
[34] splines_3.2.2      systemfit_1.1-18   pbkrtest_0.4-2    
[37] colorspace_1.2-6   quantreg_5.19      sandwich_2.3-4    
[40] stringi_0.5-5      munsell_0.4.2      chron_2.3-47      
[43] zoo_1.7-12        

Last Friday the Cologne R user group came together for the 15th time. Since its inception over three years ago the group evolved from a small gathering in a pub into an active data science community, covering wider topics than just R. Still, R is the link and clue between the different interests. Last Friday's agenda was a good example of this, with three talks touching on workflow management, web development and risk analysis.

R in a big data pipeline

Download slides

Yuki Katoh had travelled all the way from Berlin to present on how to embed R with luigi into a heterogeneous workflow of different applications. This is especially useful when R needs to be integrated with hadoop/hdfs based technologies, such as Spark and Hive. Luigi is not unlike Make, which Kirill presented at our last meeting in June. In a configuration file Yuki specified the various workflow steps and dependencies between the jobs.

Kicking off the luigi script starts the workflow, and luigid server allows Yuki to monitor the various parts of the dependency graph visually. Thus, he can see the progress of his workflow in real time and identify quickly, when and where a sub process fails. As Yuki pointed out, this becomes critical in production systems, where failures need to be known and fixed quickly, unlike when ones carries out an explorative analysis in a development/research environment. See also Yuki's blog post for further details.

Shiny + Shinyjs

Download presentation files

Shiny is a very popular R package that allows users to develop interactive browser applications. Paul Viefers introduced us to the extension shinyjs, a package written by Dean Attali. The name suggests already that the package provides additional JavaScript functionality. Indeed, it does, but without the need to learn JavaScript, as those functions are wrapped into R.

Paul showed us an example of a shinyapp that depending on the user plotted a different graph. Behind the scene his script would either hide or shows those plots, conditioned on the user. With only a few lines in R it allowed him to develop a user specific application. To achieve this he created a login screen that checks for user name and password. In his example he had hard coded the login credentials, instead of using a secure connection via a professional shiny server instance. However this was sufficient for his purpose, where he tests how students react to different economic scenarios in a lab environment at university.

Experience vs. Data

Download slides

The last talk of the meeting had a more statistical focus with examples from insurance. I repeated my talk from the LondonR user group meeting in June. One of the challenge in insurance is that despite of having many customers , insurance companies will have little claims data per customer to assess risks.

I presented some Bayesian ideas to analyse risks with little data. I used the wonderful "Hit and run accident" example from Daniel Kahneman's book Thinking, fast and slow to explain Bayes' formula, introduced Bayesian belief networks for a claims analysis and discussed the challenge of predicting events when they haven't happened yet (also in Stan). Along the way I mentioned a few ideas on communicating risk, which I learned from David Spiegelhalter earlier this year.

Next Kölner R meeting

The next meeting will be scheduled in December. Details will be published on our Meetup site. Thanks again to Revolution Analytics/Microsoft for their sponsorship.

Please get in touch, if you would like to present at the next meeting.

Photo: Arthur Charpentier

The R in Insurance conference in Amsterdam was a sold out success! Congratulations to the organising committee at the University of Amsterdam, and many thanks to our sponsors:

Milliman, RStudio, CYBAEA, Deloitte, a.s.r., Triple A Risk Finance, AEGON, Delta Lloyd Amsterdam, QBE Re and APPLIED AI

This one-day conference focused once more on applications in insurance and actuarial science that use R. Topics covered included reserving, pricing, loss modelling, the use of R in a production environment and more.

Next summer we are back in London at Cass Business School.

The slides are now available from the links in the agenda below.

Over the weekend we released version 0.2.1 of the ChainLadder package for claims reserving on CRAN.

New Features

• New function PaidIncurredChain by Fabio Concina, based on the 2010 Merz & Wüthrich paper Paid-incurred chain claims reserving method
• Functions plot.MackChainLadder and plot.BootChainLadder gained new argument which, allowing users to specify which sub-plot to display. Thanks to Christophe Dutang for this suggestion.

Output of plot(MackChainLadder(MW2014, est.sigma="Mack"), which=3:6)

Changes

• Updated NAMESPACE file to comply with new R CMD checks in R-3.3.0
• Removed package dependencies on grDevices and Hmisc
• Expanded package vignette with new paragraph on importing spreadsheet data, a new section "Paid-Incurred Chain Model" and an added example for a full claims development picture in the "One Year Claims Development Result" section, see also [1] .

Binary versions of the package will appear on the various CRAN mirrors over the next couple of days. Alternatively you can install ChainLadder directly from GitHub using the following R commands:

install.packages(c(“systemfit”, “actuar", "statmod", "tweedie", "devtools"))
library(devtools)
install_github("mages/ChainLadder")
library(ChainLadder)

Completely new to ChainLadder? Start with the package vignette.

References

[1] Claims run-off uncertainty: the full picture. (with M. Merz) SSRN Manuscript, ID 2524352, 2014.

I will be speaking at the Bay Area User Group meeting tonight about Communicating Risk. Anthony Goldbloom from Kaggle and Karim Chine from ElasticR will be there as well. The meeting will be at Microsoft in Mountain View.

Later this week I will give a similar presentation at the R in Finance conference in Chicago. Please get in touch if you are around and would like to share a coffee with me.

I continue my Stan experiments with another insurance example. Here I am particular interested in the posterior predictive distribution from only three data points. Or, to put it differently I have a customer of three years and I'd like to predict the expected claims cost for the next year to set or adjust the premium.

The example is taken from section 16.17 in Loss Models: From Data to Decisions [1]. Some time ago I used the same example to get my head around a Bayesian credibility model.

Suppose the claims likelihood distribution is believed to follow an exponential distribution for a given parameter \(\Theta\). The prior parameter distribution on \(\Theta\) is assumed to be a gamma distribution with parameters \(\alpha=4, \beta=1000\):
\[\begin{aligned}\Theta & \sim \mbox{Gamma}(\alpha, \beta)\\
\ell_i & \sim \mbox{Exp}(\Theta) , \; \forall i \in N
\end{aligned}\]In this case the predictive distribution is a Pareto II distribution with density \(f(x) = \frac{\alpha \beta^\alpha}{(x+\beta)^{\alpha+1}}\) and a mean of \(\frac{\beta}{\alpha-1}=\,\)333.33.

I have three independent observations, namely losses of $100, $950 and $450. The posterior predictive expected loss is $416.67 and can be derived analytical, as shown in my earlier post. Now let me reproduce the answer with Stan as well.

Implementing the model in Stan is straightforward and I follow the same steps as in my simple example of last week. However, here I am also interested in the posterior predictive distribution, hence I add a generated quantities code block.



The output shows a simulated predictive mean of $416.86, close to the analytical answer. I can also read out that the 75%ile of the posterior predictive distribution is a loss of $542 vs. $414 from the prior predictive. That means every four years I shouldn't be surprised to observe a loss in excess of $500. Further I note that 90% of losses are expected to be less than $950, or in other words the observation in my data may reflect the outcome of an event with a 1 in 10 return period.

Comparing the sampling output from Stan with the analytical output gives me some confidence that I am doing the 'right thing'.

References

[1] Klugman, S. A., Panjer, H. H. & Willmot, G. E. (2004), Loss Models: From Data to Decisions, Wiley Series in Probability and Statistics.

Session Info

R version 3.2.0 (2015-04-16)
Platform: x86_64-apple-darwin13.4.0 (64-bit)
Running under: OS X 10.10.3 (Yosemite)

locale:
[1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8

attached base packages:
[1] stats graphics grDevices utils datasets methods base     

other attached packages:
[1] lattice_0.20-31 actuar_1.1-8 rstan_2.6.0 inline_0.3.14  
[5] Rcpp_0.11.6    

loaded via a namespace (and not attached):
[1] tools_3.2.0  codetools_0.2-11 grid_3.2.0 stats4_3.2.0

Suppose you have to predict the probabilities of events which haven't happened yet. How do you do this?

Here is an example from the 1950s when Longley-Cook, an actuary at an insurance company, was asked to price the risk for a mid-air collision of two planes, an event which as far as he knew hadn't happened before. The civilian airline industry was still very young, but rapidly growing and all Longely-Cook knew was that there were no collisions in the previous 5 years [1].

Where do you start?

Although the probability for a mid-air collision should be very low for any given plane, the probability for an event in a year will be higher.

Let's think of the years as a series of Bernoulli trials with unknown probability \(p\). That's a likelihood. If I start with an uninformed prior, such as a Beta(\(\alpha,\beta\)) with \(\alpha=1, \beta=1\) then I can use the concept of Bayesian conjugates to update my prior believe.

In this case the posterior parameter distribution is Beta again with hyper-parameters \(\alpha'=\alpha + \sum_{i=1}^n x_i,\, \beta'=\beta + n - \sum_{i=1}^n x_i\), where \(x_i=1\) if the event occurred, or 0 otherwise and \(n\) is the number of years.

Thus, the updated parameters are \(\alpha'=1, \beta'=6\), with a posterior predictive mean of \(\alpha'/(\alpha'+\beta')=1/7\). That is a 14.3% chance for a mid-air collision in the next year with a 95% confidence interval of [0, 39%]. Or, in other words, if I round 39% to 40%, a return period of 2.5 years (1/0.4), i.e. up to 4 incidents in 10 years should be allowed for. That's what Longley-Cook predicted.

Tragically, 128 people died over the Grand Canyon in 1956, and 4 years after that, 134 people died over New York City.

Wikipedia lists 51 notable civilian mid-air collisions since 1922, including helicopters and space crafts. Since 1955 there were 11 incidents that had more than 100 fatalities, the last one in 2006.

So, what would this mean to Mr. Longley-Cook today? Well, first of all that his prediction wasn't too bad at all. Perhaps, he would set the probability at (1+11)/((1+11)+(1+60-11)\(\approx\)20% today. He may have argued that 2 x 20% = 40% of the average plane value should be included in the world wide premium for airline hull to cover mid-air collisions.

R code

Interested in the application of R in insurance? Join us at the 3rd R in Insurance conference in Amsterdam, 29 June 2015.

References

[1] Computational Actuarial Science with R, Edited by Arthur Charpentier, Chapman and Hall/CRC Reference - 656 Pages

Session Info

R version 3.2.0 (2015-04-16)
Platform: x86_64-apple-darwin13.4.0 (64-bit)
Running under: OS X 10.10.3 (Yosemite)

locale:
[1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods  
[7] base     

other attached packages:
[1] XML_3.98-1.1

loaded via a namespace (and not attached):
[1] tools_3.2.0

ChainLadder is an R package that provides statistical methods and models for claims reserving in general insurance.

With version 0.2.0 we added new functions to estimate the claims development result (CDR) as required under Solvency II. Special thanks to Alessandro Carrato, Giuseppe Crupi and Mario Wüthrich who have contributed code and documentation.

New Features

• New generic function CDR to estimate the one year claims development result. S3 methods for the Mack and bootstrap model have been added already:
  
  • CDR.MackChainLadder to estimate the one year claims development result of the Mack model without tail factor, based papers by Merz & Wüthrich (2008, 2014)
  • CDR.BootChainLadder to estimate the one year claims development result of the bootstrap model.
• New function tweedieReserve to estimate reserves in a GLM framework, including the one year claims development result.
• Package vignette has a new chapter on One Year Claims Development Result
• New example data MW2008 and MW2014 form the Merz & Wüthrich (2008, 2014) papers

Changes

• Source code development moved from Google Code to GitHub
• as.data.frame.triangle now gives warning message when dev. period is a character.
• Alessandro Carrato, Giuseppe Crupi and Mario Wüthrich have been added as authors, thanks to their major contribution to code and documentation.
• Christophe Dutang, Arnaud Lacoume and Arthur Charpentier have been added as contributors, thanks to their feedback, guidance and code contribution.

Examples

The examples below use the triangle of the 2008 Merz & Wüthrich paper and illustrate how the one year claims development result can be estimated using the new CDR function for output of MackChainLadder and BootChainLadder. Also the tweedieReserve function is demonstrated, which can estimate the one year CDR as well, by setting the argument rereserving to TRUE.

For further details see package vignette and the help pages of the respective functions.

References

Michael Merz and Mario V. Wüthrich. Modelling the claims development result for solvency purposes. CAS E-Forum, Fall:542–568, 2008

Michael Merz and Mario V. Wüthrich. Claims run-off uncertainty: the full picture. SSRN Manuscript, 2524352, 2014.

Session Info

R version 3.1.3 (2015-03-09)
Platform: x86_64-apple-darwin13.4.0 (64-bit)
Running under: OS X 10.10.2 (Yosemite)

locale:
[1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8

attached base packages:
[1] stats graphics grDevices utils datasets methods base     

other attached packages:
[1] ChainLadder_0.2.0 statmod_1.4.20 systemfit_1.1-14 lmtest_0.9-33    
[5] zoo_1.7-12        car_2.0-25     Matrix_1.1-5     

loaded via a namespace (and not attached):
 [1] acepack_1.3-3.3     actuar_1.1-8        cluster_2.0.1      
 [4] colorspace_1.2-6    digest_0.6.8        foreign_0.8-63     
 [7] Formula_1.2-0       ggplot2_1.0.0       grid_3.1.3         
[10] gtable_0.1.2        Hmisc_3.15-0        lattice_0.20-30    
[13] latticeExtra_0.6-26 lme4_1.1-7          MASS_7.3-39        
[16] mgcv_1.8-5          minqa_1.2.4         munsell_0.4.2      
[19] nlme_3.1-120        nloptr_1.0.4        nnet_7.3-9         
[22] parallel_3.1.3      pbkrtest_0.4-2      plyr_1.8.1         
[25] proto_0.3-10        quantreg_5.11       RColorBrewer_1.1-2 
[28] Rcpp_0.11.5         reshape2_1.4.1      rpart_4.1-9        
[31] sandwich_2.3-2      scales_0.2.4        SparseM_1.6        
[34] splines_3.1.3       stringr_0.6.2       survival_2.38-1    
[37] tools_3.1.3         tweedie_2.2.1

The registration for the third conference on R in Insurance on Monday 29 June 2015 at the University of Amsterdam has opened.


This one-day conference will focus again on applications in insurance and actuarial science that use R, the lingua franca for statistical computation.

The intended audience of the conference includes both academics and practitioners who are active or interested in the applications of R in insurance.

Invited talks will be given by:

• Prof. Richard Gill, Leiden University
• Dr James Guszcza, FCAS, Chief Data Scientist, Deloitte - US

Perhaps you have seen Richard's TED talk on Statistical Errors in Court or Jim's talk on Predictive Modelling and Behaviour Insight or Actuarial Analytics in R. We are thrilled that they accepted our invitation.

We invite you to submit a one-page abstract for consideration. Both academic and practitioner proposals related to R are encouraged. The submission deadline for abstracts is 28 March 2015.
Please email your abstract of no more than 300 words (in text or pdf format) to r-in-insurance@uva.nl.

Details about the registration and abstract submission are given on the dedicated R in Insurance page at the University of Amsterdam.

For more information about the past events visit www.rininsurance.com.

Taking the first step is often the hardest: getting data from Excel into R.

Suppose you would like to use the ChainLadder package to forecast future claims payments for a run-off triangle that you have stored in Excel.


How do you get the triangle into R and execute a reserving function, such as MackChainLadder?

Well, there are many ways to do this and the ChainLadder package vignette, as well as the R manual on Data Import/Export has all of the details, but here is a quick and dirty solution using a CSV-file.

Open a new Excel workbook and copy your triangle into cell A1, with the first column being the accident or origin period and the first row describing the development period or age. You find an example CSV-file on GitHub.

Make sure that your triangle has no formatting, such a commas to separate thousands, as Excel will save those cell as characters. Now open R and go through the following commands:

# The first command will open a window and 
# ask you to select your CSV-file
myCSVfile <- file.choose()
# Read file into R
dat <- read.csv(file=myCSVfile) 
# use read.csv2 if semicolons are used as a separator
# likely to be the case if you are in continental Europe

dat # to see your data

     AY   X1    X2    X3    X4    X5    X6    X7    X8    X9   X10
1  1981 5012  8269 10907 11805 13539 16181 18009 18608 18662 18834
2  1982  106  4285  5396 10666 13782 15599 15496 16169 16704    NA
3  1983 3410  8992 13873 16141 18735 22214 22863 23466    NA    NA
4  1984 5655 11555 15766 21266 23425 26083 27067    NA    NA    NA
5  1985 1092  9565 15836 22169 25955 26180    NA    NA    NA    NA
6  1986 1513  6445 11702 12935 15852    NA    NA    NA    NA    NA
7  1987  557  4020 10946 12314    NA    NA    NA    NA    NA    NA
8  1988 1351  6947 13112    NA    NA    NA    NA    NA    NA    NA
9  1989 3133  5395    NA    NA    NA    NA    NA    NA    NA    NA
10 1990 2063    NA    NA    NA    NA    NA    NA    NA    NA    NA

Ok, the data is in R, but now you have to convert it into a triangle. A triangle is basically a matrix with extra attributes. To do this execute the following steps.

# Load the ChainLadder package
library(ChainLadder)
# Ignore first column which holds accident year information 
tri <- dat[,-1]
# Convert to matrix
tri <- as.matrix(tri)
# Add dimension names
dimnames(tri) <- list(origin=dat[,1], dev=1:ncol(tri))
# Convert into a triangle class
tri <- as.triangle(tri)
tri
      dev
origin    1     2     3     4     5     6     7     8     9    10
  1981 5012  8269 10907 11805 13539 16181 18009 18608 18662 18834
  1982  106  4285  5396 10666 13782 15599 15496 16169 16704    NA
  1983 3410  8992 13873 16141 18735 22214 22863 23466    NA    NA
  1984 5655 11555 15766 21266 23425 26083 27067    NA    NA    NA
  1985 1092  9565 15836 22169 25955 26180    NA    NA    NA    NA
  1986 1513  6445 11702 12935 15852    NA    NA    NA    NA    NA
  1987  557  4020 10946 12314    NA    NA    NA    NA    NA    NA
  1988 1351  6947 13112    NA    NA    NA    NA    NA    NA    NA
  1989 3133  5395    NA    NA    NA    NA    NA    NA    NA    NA
  1990 2063    NA    NA    NA    NA    NA    NA    NA    NA    NA

With those preparations done you can execute the MackChainLadder function:

M <- MackChainLadder(tri, est.sigma = "Mack")
M
     Latest Dev.To.Date Ultimate   IBNR Mack.S.E CV(IBNR)
1981 18,834       1.000   18,834      0        0      NaN
1982 16,704       0.991   16,858    154      206    1.339
1983 23,466       0.974   24,083    617      623    1.010
1984 27,067       0.943   28,703  1,636      747    0.457
1985 26,180       0.905   28,927  2,747    1,469    0.535
1986 15,852       0.813   19,501  3,649    2,002    0.549
1987 12,314       0.694   17,749  5,435    2,209    0.406
1988 13,112       0.546   24,019 10,907    5,358    0.491
1989  5,395       0.336   16,045 10,650    6,333    0.595
1990  2,063       0.112   18,402 16,339   24,566    1.503

               Totals
Latest:    160,987.00
Dev:             0.76
Ultimate:  213,122.23
IBNR:       52,135.23
Mack S.E.:  26,909.01
CV(IBNR):        0.52

To copy the full triangle back into Excel you can use the clipboard:
write.table(M$FullTriangle, file="clipboard", sep="\t").
Go back to Excel and hit <Ctrl> + V on your keyboard to paste the data into R.

For more details see the package vignette and Dan's post on pasting triangles from Excel into R via the clipboard.

If you are after a thorough overview of R in insurance take a look at the book Computational Actuarial Science with R.

Finally, join the Special Interest Group on using R in actuarial science and insurance to share your questions and answers.

Session Info

R version 3.1.2 (2014-10-31)
Platform: x86_64-apple-darwin13.4.0 (64-bit)

locale:
[1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods  
[7] base     

other attached packages:
[1] ChainLadder_0.1.9 systemfit_1.1-14  lmtest_0.9-33    
[4] zoo_1.7-11        car_2.0-21        Matrix_1.1-4     

loaded via a namespace (and not attached):
 [1] acepack_1.3-3.3     actuar_1.1-6        cluster_1.15.3     
 [4] foreign_0.8-61      Formula_1.1-2       grid_3.1.2         
 [7] Hmisc_3.14-5        lattice_0.20-29     latticeExtra_0.6-26
[10] MASS_7.3-35         nnet_7.3-8          plyr_1.8.1         
[13] RColorBrewer_1.0-5  Rcpp_0.11.3         reshape2_1.4       
[16] rpart_4.1-8         sandwich_2.3-2      splines_3.1.2      
[19] statmod_1.4.20      stringr_0.6.2       survival_2.37-7    
[22] tools_3.1.2         tweedie_2.2.1 

Last week Arthur Charpentier sketched out a Markov spatial process to generate hurricane trajectories. Here, I would like to take another look at the data Arthur used, but focus on its time component.

According to the Insurance Information Institute, a normal season, based on averages from 1980 to 2010, has 12 named storms, six hurricanes and three major hurricanes. The usual peak months of August and September passed without any major catastrophes this year, but the Atlantic hurricane season is not over yet.

So, let's take a look at the data again, and here I will use code from Gaston Sanchez, who looked at windstorm data earlier.

I believe, I am using the same data as Arthur, but from a different source, which allows me to download it in one file (13.9MB). Using code from Gaston my chart of all named windstorms over the period of 1989 to 2013 looks like this.


Plotting the data by months illustrates the seasonality of windstorms during the year. Note, that there are no named windstorms for the months of February and March and although the season runs until the end of November, I can clearly see that the peak months are August and September.


Perhaps there are other time components that effect the seasonality across years, such as La Niña? Plotting the years 1989 to 2013 certainly shows that there are years with more windstorm activity than others. Critical to the impact and cost of windstorms is if they make landfall or not. Hence, I add information on deaths and economic damages for major hurricanes over that period from Wikipedia.


Although 1992 doesn't show much windstorm activity, hurricane Andrew was the most expensive one to that date and changed the insurance industry significantly. Following hurricane Andrew insurance companies started to embrace catastrophe models.

The economic loss is a very poor proxy to the loss of lives. In 1998 Hurricane Mitch cost the lives of over 19,000, with most of them living in Honduras. The economic cost of $6.2bn looks small compared to the cost of Andrew six years earlier ($26.5bn).


Although over the last few years we have seen a fairly benign impact of windstorm activity, the next big event can have a much more sever impact than what we have seen historically, as the population (and economy) on the Gulf of Mexico has and is growing rapidly, 150% from 1960 to 2008 alone. A hurricane season causing damages over $200bn doesn't look unreasonable anymore.

R Code

Session Info

R version 3.1.1 (2014-07-10)
Platform: x86_64-apple-darwin13.1.0 (64-bit)

locale:
[1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8

attached base packages:
[1] grid      stats     graphics  grDevices utils     datasets 
[7] methods   base     

other attached packages:
[1] XML_3.98-1.1     data.table_1.9.2 ggplot2_1.0.0   
[4] maps_2.3-7      

loaded via a namespace (and not attached):
 [1] colorspace_1.2-4 digest_0.6.4     gtable_0.1.2    
 [4] labeling_0.3     MASS_7.3-33      munsell_0.4.2   
 [7] plyr_1.8.1       proto_0.3-10     Rcpp_0.11.2     
[10] reshape2_1.4     scales_0.2.4     stringr_0.6.2   
[13] tools_3.1.1 

Over the weekend we released version 0.1.8 of the ChainLadder package for claims reserving on CRAN.

What is claims reserving?

The insurance industry, unlike other industries, does not sell products as such but promises. An insurance policy is a promise by the insurer to the policyholder to pay for future claims for an upfront received premium.

As a result insurers don't know the upfront cost for their service, but rely on historical data analysis and judgement to predict a sustainable price for their offering. In General Insurance (or Non-Life Insurance, e.g. motor, property and casualty insurance) most policies run for a period of 12 months. However, the claims payment process can take years or even decades. Therefore often not even the delivery date of their product is known to insurers. The money set aside for those future claims payments are called reserves.

The 2nd R in Insurance conference took place last Monday, 14 July, at Cass Business School London.

This one-day conference focused once more on applications in insurance and actuarial science that use R. Topics covered included reserving, pricing, loss modelling, the use of R in a production environment and more.

In the first plenary session, Montserrat Guillen (Riskcenter, University of Barcelona) and Leo Guelman (Royal Bank of Canada, RBC Insurance) spoke about the rise of uplift models. These predictive models are used for improved targeting of policyholders by marketing campaigns, through the use of experimental data. The presenters illustrated the use of their uplift package (available on CRAN), which they have developed for such applications.

The registration for the 2nd R in Insurance conference at Cass Business School London will close this Friday, 4 July.

The programme includes talks from international practitioners and leading academics, see below. For more details and registration visit: http://www.rininsurance.com.

The registration for the second conference on R in Insurance on Monday 14 July 2014 at Cass Business School in London has opened.

This one-day conference will focus again on applications in insurance and actuarial science that use R, the lingua franca for statistical computation. Topics covered may include actuarial statistics, capital modelling, pricing, reserving, reinsurance and extreme events, portfolio allocation, advanced risk tools, high-performance computing, econometrics and more. All topics will be discussed within the context of using R as a primary tool for insurance risk management, analysis and modelling.

The intended audience of the conference includes both academics and practitioners who are active or interested in the applications of R in insurance.

Invited talks will be given by:

• Arthur Charpentier, Département de mathématiques Université du Québec à Montréal
• Montserrat Guillen, Dept. Econometrics University of Barcelona together with Leo Guelman, Royal Bank of Canada (RBC Insurance division)

Attendance of the whole conference is the equivalent of 6.5 hours of CPD for members of the Actuarial Profession.

We invite you to submit a one-page abstract for consideration. Both academic and practitioner proposals related to R are encouraged. The submission deadline for abstracts is 28 March 2014.

Details about the registration and abstract submission are given on the dedicated R in Insurance page at Cass Business School.

Sponsors

The organisers, Andreas Tsanakas and Markus Gesmann, gratefully acknowledge the sponsorship of Mango Solutions, Cybaea, PwC and RStudio.



Last year's programme, abstracts and talks are available online.