A Revisit of the Optimal Excess-of-Loss Contract

TL;DR

This paper revisits the optimal Excess-of-Loss reinsurance contract, addressing issues with Stop-Loss reinsurance and providing estimators and analysis under various assumptions with both simulated and real data.

Contribution

It introduces a new focus on Excess-of-Loss reinsurance, offers estimators for optimal contracts, and analyzes their statistical properties under diverse conditions.

Findings

Optimal Excess-of-Loss reinsurance avoids zero insolvency probability.

Provided estimators with proven statistical properties.

Validated findings with simulated and real-world data.

Abstract

It is well-known that Excess-of-Loss reinsurance has more marketability than Stop-Loss reinsurance, though Stop-Loss reinsurance is the most prominent setting discussed in the optimal (re)insurance design literature. We point out that optimal reinsurance policy under Stop-Loss leads to a zero insolvency probability, which motivates our paper. We provide a remedy to this peculiar property of the optimal Stop-Loss reinsurance contract by investigating the optimal Excess-of-Loss reinsurance contract instead. We also provide estimators for the optimal Excess-of-Loss and Stop-Loss contracts and investigate their statistical properties under many premium principle assumptions and various risk preferences, which according to our knowledge, have never been investigated in the literature. Simulated data and real-life data are used to illustrate our main theoretical findings.