Research On The Original Insurance Pricing Problem Based On BSDE Model

Insurance pricing in the insurance industry has always been an important topic in asset pricing research,and the pricing research and application of primary insurance is particularly important.With the development of the theory of Backward Stochastic Differential Equation(BSDE)and its application in the pricing of financial assets,it also provides a new idea for the pricing of insurance.The research of this paper will be divided into the following four parts:Firstly,the wealth model of assets is constructed by using the thinking of investment portfolio,and two important parameters affecting the insurance premium rate,namely the expense ratio of the company's operation and the reserve ratio of outstanding compensation,are added into it,and the pricing formula is obtained by solving the corresponding partial differential equation.Second,the fixed interest rate of risk-free assets in the portfolio is extended to a random interest rate,that is,Vasicek model is introduced to establish a pricing equation.Thirdly,by introducing the time delay effect into the risk assets(stock assets)in the portfolio,the backward Stochastic Differential Equation(ASDE)with time delay is obtained,pricing formula is obtained by constructing the dual Advanced Stochastic Differential Equation(ASDE)and the martingale method.The innovation of this paper is to combine the backward stochastic differential equation with the original insurance pricing and introduce the operating expense ratio and the outstanding compensation reserve ratio to make the model more realistic.The different pricing processes when the interest rate in risk-free assets is stochastic and the risk assets satisfy the time-delay effect are discussed respectively.