The equilibrium strategy of insurance companies’ dividends and reinsurance games

Abstract

We investigated the optimal risk management strategies of an insurance company within a two-player non-cooperative differential game framework. The key feature of this model is considering the company’s surplus as a strategic variable to make the insurance company more attractive to shareholders. In this setup, shareholders are participants who demand a share of the surplus, while managers are participants concerned with the risk management of the surplus. The objective of the shareholders is to maximize the expected discounted dividends. We address this asymmetric game under two different assumptions about the managers’ objectives: in the first scenario, the managers aim to minimize the probability of bankruptcy; in the second scenario, the managers aim to maximize the expected discounted utility derived from the surplus.