The Optimal Problem Of Investment-reinsurance With Stochastic Volatilities

In this thesis,we study the optimal problem of investment-reinsurance with stochastic volatilities.In chapter one,we consider the optimal problem of investment-reinsurance under multiassets,assume that the insurer has investment and reinsurance.The wealth process consists of surplus process of reinsurance and earnings of investments.While the equation of assets have fast stochastic volatility and slow stochastic volatility respectively,we give HJB equation about objective function.We consider using the singular perturbation method to give approximate solution,and obtain the optimal strategy of insurer.In chapter two,we study the extended Heston model under the multi-scale stochastic volatilities,giving the solution of HJB equation,using the mathematical method and obtaining the robust optimal control of insurer.