Ruin probability for heavy-tailed and dependent losses under reinsurance strategies

Abstract

The frequency and severity of extreme events have increased in recent years in many areas. In the context of risk management for insurance companies, reinsurance provides a safe solution as it offers coverage for large claims. This paper investigates the impact of dependent extreme losses on ruin probabilities under four types of reinsurance: excess of loss, quota share, largest claims, and ecomor. To achieve this, we use the dynamic GARCH-EVT-Copula combined model to fit the specific features of claim data and provide more accurate estimates compared to classical models. We derive the surplus processes and asymptotic ruin probabilities under the Cramér–Lundberg risk process. Using a numerical example with real-life data, we illustrate the effects of dependence and the behavior of reinsurance strategies for both insurers and reinsurers. This comparison includes risk premiums, surplus processes, risk measures, and ruin probabilities. The findings show that the GARCH-EVT-Copula model mitigates the over- and under-estimation of risk associated with extremes and lowers the ruin probability for heavy-tailed distributions.