Over the last year I worked with Jake Morris on a research paper for the Casualty Actuarial Society. We are delighted to see it published:
Gesmann, M., and Morris, J. “Hierarchical Compartmental Reserving Models.” Casualty Actuarial Society, CAS Research Papers, 19 Aug. 2020, https://www.casact.org/sites/default/files/2021-02/compartmental-reserving-models-gesmannmorris0820.pdf
The paper demonstrates how one can describe the dynamics of claims processes with differential equations and probability distributions. All of this is set into a Bayesian framework that allows us to combine judgement and historical data into a consistent framework.
At the Insurance Data Science conference, both Eric Novik and Paul-Christian Bürkner emphasised in their talks the value of thinking about the data generating process when building Bayesian statistical models. It is also a key step in Michael Betancourt’s Principled Bayesian Workflow.
In this post, I will discuss in more detail how to set priors, and review the prior and posterior parameter distributions, but also the prior predictive distributions with brms (Bürkner (2017)).
Ahead of the Stan Workshop on Tuesday, here is another example of using brms (Bürkner (2017)) for claims reserving. This time I will use a model inspired by the 2012 paper A Bayesian Nonlinear Model for Forecasting Insurance Loss Payments (Zhang, Dukic, and Guszcza (2012)), which can be seen as a follow-up to Jim Guszcza’s Hierarchical Growth Curve Model (Guszcza (2008)).
I discussed Jim’s model in an earlier post using Stan.
This is a follow-up post on hierarchical compartmental reserving models using PK/PD models. It will show how differential equations can be used with Stan/ brms and how correlation for the same group level terms can be modelled.
PK/ PD is usually short for pharmacokinetic/ pharmacodynamic models, but as Eric Novik of Generable pointed out to me, it could also be short for Payment Kinetics/ Payment Dynamics Models in the insurance context.
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).
Last week I wrote about Glenn Meyers’ correlated log-normal chain-ladder model (CCL), which he presented at the 10th Bayesian Mixer Meetup. Today, I will continue with a variant Glenn also discussed: The changing settlement log-normal chain-ladder model (CSR).
Glenn used the correlated log-normal chain-ladder model on reported incurred claims data to predict future developments.
However, when looking at paid claims data, Glenn suggested to change the model slightly. Instead allowing for correlation across accident years, he allows for a gradual shift in the payout pattern to account for a change in the claim settlement rate across accident years.
On 23 November Glenn Meyers gave a fascinating talk about The Bayesian Revolution in Stochastic Loss Reserving at the 10th Bayesian Mixer Meetup in London. Glenn worked for many years as a research actuary at Verisk/ ISO, he helped to set up the CAS Loss Reserve Database and published a monograph on Stochastic loss reserving using Bayesian MCMC models.
In this blog post I will go through the Correlated Log-normal Chain-Ladder Model from his presentation.
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.
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.
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.