When is truncated stop loss optimal?

TL;DR

This paper analyzes the conditions under which truncated stop loss reinsurance contracts are optimal, balancing profit and risk, and finds these conditions are generally met in practical scenarios.

Contribution

It derives specific conditions for the optimality of truncated stop loss reinsurance and argues these are typically satisfied in real-world markets.

Findings

Optimality conditions are derived for truncated stop loss contracts.

Reinsurance is usually not too cheap, supporting the practical relevance of the results.

Conditions for optimality are generally satisfied in practice.

Abstract

The paper examines how reinsurance can be used to strike a balance between expected profit and VaR/CVaR risk. Conditions making truncated stop loss contracts optimal are derived, and it is argued that those are usually satisfied in practice. One of the prerequisites is that reinsurance is not too cheap, and an argument resembling arbitrage suggests that it is not.