Stochastic Loss Reserving: Dependence and Estimation

TL;DR

This paper introduces a modified continuous generalized method of moments (CGMM) for loss reserving that effectively estimates complex dependence models, including those without closed-form likelihoods, offering a practical alternative to maximum likelihood estimation.

Contribution

It applies a novel CGMM approach to loss reserving, enabling estimation of complex dependence models like stable distributions that are difficult to handle with traditional methods.

Findings

CGMM provides comparable estimates to MLE where MLE is impractical.

The method successfully estimates models with intractable likelihoods.

Application to models from Avanzi et al. and stable distributions demonstrates effectiveness.

Abstract

Nowadays insurers have to account for potentially complex dependence between risks. In the field of loss reserving, there are many parametric and non-parametric models attempting to capture dependence between business lines. One common approach has been to use additive background risk models (ABRMs) which provide rich and interpretable dependence structures via a common shock model. Unfortunately, ABRMs are often restrictive. Models that capture necessary features may have impractical to estimate parameters. For example models without a closed-form likelihood function for lack of a probability density function (e.g. some Tweedie, Stable Distributions, etc). We apply a modification of the continuous generalised method of moments (CGMM) of [Carrasco and Florens, 2000] which delivers comparable estimators to the MLE to loss reserving. We examine models such as the one proposed by [Avanzi et al., 2016] and a related but novel one derived from the stable family of distributions. Our CGMM method of estimation provides conventional non-Bayesian estimates in the case where MLEs are impractical.