reserving

It is exactly one year ago that the Casualty Actuarial Society published our research paper on Hierarchical Compartmental Reserving Models (Gesmann and Morris (2020)). One aspect we looked into was the question if the choice of modelling cumulative or incremental payment data over time matters. Many traditional reserving methods (including the chain-ladder technique) take cumulative claims triangles as an input. Plotting cumulative claims data allows us to quickly understand key data features by eye.

Today, I will sketch out ideas from the Hierarchical Compartmental Models for Loss Reserving paper by Jake Morris, which was published in the summer of 2016 (Morris (2016)). Jake’s model is inspired by PK/PD models (pharmacokinetic/pharmacodynamic models) used in the pharmaceutical industry to describe the time course of effect intensity in response to administration of a drug dose. The hierarchical compartmental model fits outstanding and paid claims simultaneously, combining ideas of Clark (2003), Quarg and Mack (2004), Miranda, Nielsen, and Verrall (2012), Guszcza (2008) and Zhang, Dukic, and Guszcza (2012).

Statistical Methods and Models for Claims Reserving in General Insurance.

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 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.

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.

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.

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.

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.

There can never be too many examples for transforming data with R. So, here is another example of reshaping a data.frame into a matrix. Here I have a data frame that shows incremental claim payments over time for different loss occurrence (origin) years. The format of the data frame above is how this kind of data is usually stored in a data base. However, I would like to see the payments of the different origin years in rows of a matrix.

Version 0.1.6 of the ChainLadder package has been released and is already available from CRAN. The new version adds the function CLFMdelta. CLFMdelta finds consistent weighting parameters delta for a vector of selected age-to-age chain-ladder factors for a given run-off triangle. The added functionality was implemented by Dan Murphy, who is the co-author of the paper A Family of Chain-Ladder Factor Models for Selected Link Ratios by Bardis, Majidi, Murphy.

Last week we released version 0.1.5-6 of the ChainLadder package on CRAN. The ChainLadder package provides statistical models, which are typically used for the estimation of outstanding claims reserves in general insurance. The package vignette gives an overview of the package functionality. Output of plot(MackChainLadder(GenIns)) Since the last CRAN release Dan Murphy added new features to the MackChainLadder function and we fixed a bug in BootChainLadder.

This is the third post about Christofides’ paper on Regression models based on log-incremental payments [1]. The first post covered the fundamentals of Christofides’ reserving model in sections A - F, the second focused on a more realistic example and model reduction of sections G - K. Today’s post will wrap up the paper with sections L - M and discuss data normalisation and claims inflation. I will use the same triangle of incremental claims data as introduced in my previous post.

Following on from last week’s post I will continue to go through the paper Regression models based on log-incremental payments by Stavros Christofides [1]. In the previous post I introduced the model from the first 15 pages up to section F. Today I will progress with sections G to K which illustrate the model with a more realistic incremental claims payments triangle from a UK Motor Non-Comprehensive account: # Page D5.

A recent post on the PirateGrunt blog on claims reserving inspired me to look into the paper Regression models based on log-incremental payments by Stavros Christofides [1], published as part of the Claims Reserving Manual (Version 2) of the Institute of Actuaries. The paper is available together with a spreadsheet model, illustrating the calculations. It is very much based on ideas by Barnett and Zehnwirth, see [2] for a reference.

Last week we released version 0.1.5-4 of the ChainLadder package on CRAN. The R package provides methods which are typically used in insurance claims reserving. If you are new to R or insurance check out my recent talk on Using R in Insurance. The chain-ladder method which is a popular method in the insurance industry to forecast future claims payments gave the package its name. However, the ChainLadder package has many other reserving methods and models implemented as well, such as the bootstrap model demonstrated below.

Today we published version 0.1.5-1 of the ChainLadder package for R. It provides methods which are typically used in insurance claims reserving to forecast future claims payments. Claims development and chain-ladder forecast of the RAA data set using the Mack method The package started out of presentations given at the Stochastic Reserving Seminar at the Institute of Actuaries in 2007, 2008 and 2010, followed by talks at CAS meetings in 2008 and 2010.