An Optimal Combination of Proportional and Stop-Loss Reinsurance Contracts From Insurer's and Reinsurer's Viewpoints

TL;DR

This paper introduces a new proportional-stop-loss reinsurance contract that balances the interests of both insurer and reinsurer, optimizing parameters to maximize their expected surpluses.

Contribution

It proposes a novel combined reinsurance contract and develops a method to estimate its parameters for mutual benefit.

Findings

The new contract effectively balances insurer and reinsurer interests.

Parameters can be estimated to maximize expected surpluses.

The contract exhibits desirable risk-sharing characteristics.

Abstract

A reinsurance contract should address the conflicting interests of the insurer and reinsurer. Most of existing optimal reinsurance contracts only considers the interests of one party. This article combines the proportional and stop-loss reinsurance contracts and introduces a new reinsurance contract called proportional-stop-loss reinsurance. Using the balanced loss function, unknown parameters of the proportional-stop-loss reinsurance have been estimated such that the expected surplus for both the insurer and reinsurer are maximized. Several characteristics for the new reinsurance are provided.