Optimal Reinsurance under Endogenous Default and Background Risk

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.

💡 Research Summary

This paper investigates the optimal reinsurance problem for a utility‑maximizing insurer when the reinsurer may default endogenously and is exposed to a random background risk. An endogenous default occurs whenever the contractual indemnity demanded by the insurer exceeds the reinsurer’s available reserve at the contract’s maturity; the reserve itself is random because it incorporates a background risk component. The authors consider a one‑period setting with a non‑negative insured loss (X) (bounded above) and a background‑risk random variable (S) that captures the reinsurer’s financial or other exogenous shocks. The reinsurer charges a premium according to the expected‑value principle, (\pi(I)=(1+\eta)\mathbb{E}