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).
Following five R in Insurance conferences, we are organising the first Insurance Data Science conference at Cass Business School London, 16 July 2018.
In 2013, we started with the aim to bring practitioners of industry and academia together to discuss and exchange ideas and needs from both sides.
R was and is a perfect glue between the two groups, a tool which both side embrace and which has fostered the knowledge transfer between the two.
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 Meyers speaking at the Bayesian Mixer
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.