Abouzar Bazyari

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-extreme value theory-copula‎ ‎combined model to fit the specific features of claim data and provide more accurate estimates‎ ‎than classical models‎. ‎We derive the surplus processes and asymptotic ruin probabilities ‎under the Cramer-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-extreme value theory-copula model mitigates the over‎- ‎and under-estimation‎ ‎of risk associated with extremes and lowers the ruin probability for heavy-tailed distributions‎.