Model uncertainty in claims reserving within Tweedie's compound Poisson models

TL;DR

This paper investigates claims reserving using Tweedie's compound Poisson models, comparing methods that incorporate model uncertainty through maximum likelihood and Bayesian approaches, and explores model selection and averaging techniques.

Contribution

It introduces a comprehensive comparison of reserving estimates with and without model uncertainty, including model selection and averaging within Tweedie's framework.

Findings

Incorporating model uncertainty affects reserve estimates significantly.

Bayesian methods provide a flexible approach to model averaging.

Model selection impacts the accuracy of claims reserving.

Abstract

In this paper we examine the claims reserving problem using Tweedie's compound Poisson model. We develop the maximum likelihood and Bayesian Markov chain Monte Carlo simulation approaches to fit the model and then compare the estimated models under different scenarios. The key point we demonstrate relates to the comparison of reserving quantities with and without model uncertainty incorporated into the prediction. We consider both the model selection problem and the model averaging solutions for the predicted reserves. As a part of this process we also consider the sub problem of variable selection to obtain a parsimonious representation of the model being fitted.