Actuarial Applications and Estimation of Extended~CreditRisk$^+$

TL;DR

This paper presents a new stochastic mortality model that jointly forecasts death causes, links to an extended credit risk model for precise risk aggregation, and enables exact calculation of risk measures in insurance portfolios.

Contribution

It introduces a flexible additive mortality model integrated with an extended CreditRisk$^+$ framework, enabling exact risk calculations and applications in insurance and solvency modeling.

Findings

Efficient risk aggregation via Panjer recursion.

Exact calculation of risk measures like VaR and ES.

Successful application to Austrian and Australian data.

Abstract

We introduce an additive stochastic mortality model which allows joint modelling and forecasting of underlying death causes. Parameter families for mortality trends can be chosen freely. As model settings become high dimensional, Markov chain Monte Carlo (MCMC) is used for parameter estimation. We then link our proposed model to an extended version of the credit risk model CreditRisk$^+$. This allows exact risk aggregation via an efficient numerically stable Panjer recursion algorithm and provides numerous applications in credit, life insurance and annuity portfolios to derive P\&L distributions. Furthermore, the model allows exact (without Monte Carlo simulation error) calculation of risk measures and their sensitivities with respect to model parameters for P\&L distributions such as value-at-risk and expected shortfall. Numerous examples, including an application to partial internal models under Solvency II, using Austrian and Australian data are shown.