The Research Of Optimal Reinsurance And Investment Under Constant Elasticity Variance Model

As the vigorous development of insurance industry, the market scale gradually expands andthe risk the insurance companies face increases. In order to spread the risks andstabilize operation, insurance companies need to take measures of reinsurance to transfer a partof risks out. Risk reduction must be accompanied by the apportionment of premiums, whichmean that insurance companies’ profitable capital will decrease. Therefore, insurance companiesrequire balance between benefits and risks in reinsurance. For the purpose of benefits acquisition,at the same time, insurance companies can invest a few accumulated premiums to thefinancial market to obtain a higher expected return. However, investment bring risk. It willinevitably face the decision problem about returns and risks. So it is crucial to explore theoptimal reinsurance and investment strategy for the development of insurance company.Based on stochastic optimal control theory, this paper establishes a dynamic programmingmodel to solve the optimal reinsurance and investment issues. We firstly introduce reinsurance tothe diffusion risk model. When insurance company invest its surplus to risk-free assets or riskassets which are described by constant elasticity variation (CEV) model, through dynamicprogramming principle we can get the HJB equation with maximizing expected utility as theobjective function. Next, in different utility functions we obtain the optimal reinsurance andinvestment strategies with Legendre change-dual approach. Finally, values and images arecombined to analyze the relationship between some related parameters and the optimalreinsurance investment strategies.