Optimal Reinsurance-investment Strategy For Mean-variance Insurers Under 4/2 Stochastic Volatility Model

In recent years there are many works on optimal investment-reinsurance strategy for insurers under different SV models.As far as we know,except Shen and Zeng(2015),there is no literature consider the optimal precommitment investment-reinsurance strategy for mean-variance insurers under the SV models.Recently,Grasselli(2016)proposes a new SV model,called the 4/2(that is,1/2+3/2)SV model,which assumes that the instaneous variance is a linear combination of the 1/2 and the 3/2 terms.So it combines the properties of both Heston' s SV and 3/2 models.In addition,the 4/2 model has some new features that is not contemplated in Heston' s SV model and 3/2 model.In view of the advantages of the 4/2 SV model,in this paper we try to consider the optimal reinsurance-investment strategy for a mean-variance insurer under it.Specially,we assume that the surplus of the insurer is described by a jump-diffusion model,the financial market consists of one risk-free asset and one risky asset whose price process modeled by the 4/2 SV model,and the insurer can purchase proportional reinsurance and invest in the financial market to maximize the expectation and minimize the variance of of its terminal wealth.Firstly,using the parametrix method introduced in Levi(1907),we derive the closed-form solution of the PPDE.Then by Lagrangian duality method and the solution of the PPDE,we derive the closed-expressions of the efficient strategy and efficient frontier of our original problem.Finally,we consider some special cases of our model and results,such as the cases of Heston' s SV model and 3/2 model.