On Optimal Reinsurance Policy with Distortion Risk Measures and Premiums

TL;DR

This paper develops a unified framework for optimal reinsurance design using distortion risk measures and premiums, characterizing optimal contracts with simple marginal indemnification functions.

Contribution

It introduces a novel characterization of optimal reinsurance contracts via marginal indemnification functions that only take values zero and one.

Findings

Optimal reinsurance design can be formulated similarly for ceding, reinsurance, and social planner.

Optimal contracts have marginal indemnification functions that are binary (0 or 1).

Market preferences, premiums, and total risk are analytically separated.

Abstract

In this paper, we consider the problem of optimal reinsurance design, when the risk is measured by a distortion risk measure and the premium is given by a distortion risk premium. First, we show how the optimal reinsurance design for the ceding company, the reinsurance company and the social planner can be formulated in the same way. Second, by introducing the marginal indemnification functions, we characterize the optimal reinsurance contracts. We show that, for an optimal policy, the associated marginal indemnification function only takes the values zero and one. We will see how the roles of the market preferences and premiums and that of the total risk are separated.