I continue with the growth curve model for loss reserving from last week’s post. Today, following the ideas of James Guszcza  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 , 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  and James Guszcza .
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.
This is the third post about Christofides’ paper on Regression models based on log-incremental payments . 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 . 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 D5.17
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 , published as part of the Claims Reserving Manual (Version 2) of the Institute of Actuaries.
The paper is available together with a spread sheet model, illustrating the calculations. It is very much based on ideas by Barnett and Zehnwirth, see  for a reference.