Total loss estimation using copula-based regression models

TL;DR

This paper introduces a copula-based regression framework for accurately estimating total insurance loss by modeling dependence between claims and sizes, addressing biases from independence assumptions.

Contribution

It develops a flexible joint modeling approach combining copulae with generalized linear models and proposes a method for selecting the best copula, improving loss estimation accuracy.

Findings

Dependence modeling reduces bias in loss estimates.

The proposed method is efficient and adaptable to different copula families.

Application to car insurance demonstrates practical effectiveness.

Abstract

We present a joint copula-based model for insurance claims and sizes. It uses bivariate copulae to accommodate for the dependence between these quantities. We derive the general distribution of the policy loss without the restrictive assumption of independence. We illustrate that this distribution tends to be skewed and multi-modal, and that an independence assumption can lead to substantial bias in the estimation of the policy loss. Further, we extend our framework to regression models by combining marginal generalized linear models with a copula. We show that this approach leads to a flexible class of models, and that the parameters can be estimated efficiently using maximum-likelihood. We propose a test procedure for the selection of the optimal copula family. The usefulness of our approach is illustrated in a simulation study and in an analysis of car insurance policies.