Optimal Reinsurance under Endogenous Default and Background Risk

TL;DR

This paper derives an analytical solution for optimal reinsurance contracts considering the reinsurer's endogenous default risk and background risk, revealing their joint impact on reinsurance demand.

Contribution

It introduces a novel analytical framework for optimal reinsurance under endogenous default and background risk, differentiating contract types based on indemnity dependence.

Findings

Analytical solutions for two types of reinsurance contracts.

Reinsurer's default and background risk significantly influence reinsurance demand.

Joint effects of default and background risk alter optimal contract structures.

Abstract

This paper studies an optimal reinsurance problem for a utility-maximizing insurer, subject to the reinsurer's endogenous default and background risk. An endogenous default occurs when the insurer's contractual indemnity exceeds the reinsurer's available reserve, which is random due to the background risk. We obtain an analytical solution to the optimal contract for two types of reinsurance contracts, differentiated by whether their indemnity functions depend on the reinsurer's background risk. The results shed light on the joint effect of the reinsurer's default and background risk on the insurer's reinsurance demand.