Optimal Dividend and reinsurance strategy of a Property Insurance Company under Catastrophe Risk

TL;DR

This paper develops a novel model for property insurance companies that incorporates catastrophe risk, optimizing reinsurance and dividend strategies using mixed control of jump diffusions to maximize dividends before bankruptcy.

Contribution

It introduces the first model considering catastrophe risk in property insurance, deriving optimal control strategies through mixed singular-regular control methods.

Findings

Optimal reinsurance and dividend strategies are derived.

Catastrophe risk significantly impacts the optimal control policies.

Model results show how key parameters influence company strategies.

Abstract

We consider an optimal control problem of a property insurance company with proportional reinsurance strategy. The insurance business brings in catastrophe risk, such as earthquake and flood. The catastrophe risk could be partly reduced by reinsurance. The management of the company controls the reinsurance rate and dividend payments process to maximize the expected present value of the dividends before bankruptcy. This is the first time to consider the catastrophe risk in property insurance model, which is more realistic. We establish the solution of the problem by the mixed singular-regular control of jump diffusions. We first derive the optimal retention ratio, the optimal dividend payments level, the optimal return function and the optimal control strategy of the property insurance company, then the impacts of the catastrophe risk and key model parameters on the optimal return function and the optimal control strategy of the company are discussed.