Modeling and measuring incurred claims risk liabilities for a multi-line property and casualty insurer

TL;DR

This paper introduces a comprehensive stochastic model for multi-line property and casualty insurers to accurately measure incurred claims liabilities, capture empirical loss ratio behaviors, and optimize capital allocation under IFRS 17 standards.

Contribution

The paper presents a novel integrated modeling framework combining GLMs, autocorrelation, and copulas for multi-line loss ratio dynamics and risk measurement.

Findings

Model reproduces empirical loss ratio properties

Quantifies diversification benefits in capital requirements

Demonstrates application with real car insurance data

Abstract

We propose a stochastic model allowing property and casualty insurers with multiple business lines to measure their liabilities for incurred claims risk and calculate associated capital requirements. Our model includes many desirable features which enable reproducing empirical properties of loss ratio dynamics. For instance, our model integrates a double generalized linear model relying on accident semester and development lag effects to represent both the mean and dispersion of loss ratio distributions, an autocorrelation structure between loss ratios of the various development lags, and a hierarchical copula model driving the dependence across the various business lines. The model allows for a joint simulation of loss triangles and the quantification of the overall portfolio risk through risk measures. Consequently, a diversification benefit associated to the economic capital requirements can be measured, in accordance with IFRS 17 standards which allow for the recognition of such benefit. The allocation of capital across business lines based on the Euler allocation principle is then illustrated. The implementation of our model is performed by estimating its parameters based on a car insurance data obtained from the General Insurance Statistical Agency (GISA), and by conducting numerical simulations whose results are then presented.