A Study Of Optimal Reinsurance And Decentralized Strategy For Insurance Funds

Insurance funds are characterized by their large size and high security requirements.How to optimize returns as well as enhance their safety extends a lot of researchable issues.In order to achieve sound long-term returns,insurance companies usually allocate their funds to multiple specialized asset managers for investment,i.e.,decentralized invesment,and when facing high claims risk,insurance companies can choose to purchase reinsurance to disperse and transfer part of the risk.Based on this,this paper focuses on the optimal reinsurance and decentralized investment strategies of insurance funds.Suppose that the surplus process of insurance companies follows the Cramér-Lundberg model.Insurance companies can diversify their risks by purchasing proportional reinsurance while paying corresponding premiums to reinsurance companies.In this paper,two types of investment are considered: centralized investment and decentralized investment.For centralized investment,insurance companies centrally allocate their funds and consider the optimal reinsurance-investment strategy that maximizes the expected utility of the terminal wealth.For decentralized investment,the asset allocation of the insurance companies are divided into two steps.First,insurance companies allocate their funds to two highly specialized asset managers.Second,the asset managers invest these funds in their familiar assets.With the objective of maximizing the expected utility of terminal wealth for both insurance companies and asset managers,we obtain explicit solutions for the optimal decentralized investment strategy and the optimal reinsurance ratio by using stochastic optimal control theory and solving the corresponding Hamilton-Jacobi-Bellman(HJB)equation.To extend the application value of this paper,we also consider more general financial markets where the return rate of risky assets ?(X)varies over time and can be predicted by a set of common state variables,where the state variable X satisfies the Ornstein-Uhlenbeck(OU)process.Optimal centralized and decentralized investment strategies and optimal proportional reinsurance strategy for insurance funds under parameter time-varying scenarios are obtained under the objective of maximizing expected utility of terminal wealth.The results show that parameter time-varying financial markets allow asset managers to implement more aggressive strategies that can increase the value of asset management.Finally,the effects of the model parameters on the optimal proportional reinsurance strategy and the optimal decentralized investment strategy of insurance funds under the two financial markets are compared and analyzed through numerical simulations.