Insurance Pricing Method Of Backward Stochastic Differential Equations

Insurance pricing is crucial to gain profit for an insurance company.Thus an important direction of research is to find a suitable insurance price.With the development of backward stochastic differential equation,we can utilize it to find an investment portfolio to meet the future investment target.Because the risk loss can be deduced by the estimated risk probability through the historical data,we can arrange the investment portfolio to gain enough fund for the decided future risk loss.In this paper,in order to enlarge the range of applications of insurance pricing formula of BSDE,we improve the pricing formula by incorporating the rate of outstanding loss reserve and the expense rate of an insurance company.In the part of empirical research of the expense rate,time series method was used to establish an suitable model and the parameters were estimated through it too.For the ratio of outstanding loss reserve,we estimated it by regression analysis.Eventually,we make an evaluation by taking the estimated parameters into the solution of the adjusted backward stochastic differential equation,in order to forecast the insurance premium for the vehicle insurance.