A Copula-Based family of Bivariate Composite Models for Claim Severity Modelling

TL;DR

This paper introduces a flexible family of bivariate composite models using copulas to jointly model different claim types and costs, demonstrated with insurance data.

Contribution

It proposes a new copula-based framework for bivariate composite claim modeling, combining various marginal distributions with copulas for improved flexibility.

Findings

Models fitted successfully to insurance data

Parameters estimated using inference functions for margins

Demonstrates effectiveness in modeling claim severity

Abstract

In this paper, we consider bivariate composite models for modeling jointly different types of claims and their associated costs in a flexible manner. For expository purposes, the Gumbel copula is paired with the composite Weibull-Inverse Weibull, Paralogistic-Inverse Weibull, and Inverse Burr-Inverse Weibull marginal models. The resulting bivariate copula-based composite models are fitted on motor insurance bodily injury and property damage data from a European motor insurance company and their parameters are estimated via the inference functions for margins method.