The Application Of Backward Stochastic Differential Equations In China's Life Insurance Pricing

The compensation process is a key factor in the pricing of life insurance.In actuarial mathematics,the payment process p(t):P(t)= ?0tH(s,S(s))np(s)ds +?0tG(s,S(s))np(s)?(s)ds+ F(S(T))np(T)I{t=T},0?t?T.(0.2)For insurance companies,how to determine the current relatively fixed insurance premium rate for future uncertain payments will become a daunting task for insurance companies.At present,in insurance practice,insurance premium rates are usually determined on the basis of the equivalence principle,i.e.E[L]= 0,where L is the loss random variable.With the development of financial markets,the channels for the use of insurance funds continue to widen.To create more value,the insurance industry began to pay attention to the use of insurance funds.Various financial instruments(equities,options,futures,etc.)are widely used.In 1990,Pardoux and Peng proposed the nonlinear structure of backward s-tochastic differential equations and proved the existence and uniqueness of the equations.Backward stochastic differential equations not only have good math-ematical properties,but also have important applications in the financial field.Peng,Ei Karoui and Quenez have found that the theoretical price of many derived securities in financial markets can be solved using backward stochastic differential equations.Based on the idea of backwards and the inspiration from the application of backward stochastic differential equations,this paper improves the discrete life insurance pricing model of discrete backward stochastic differential equations from the perspective of the use of insurance funds to determine the equilibrium premium of life insurance products.Numerical experiments show that the discrete backward stochastic differential equation life insurance pricing model can not only provide the insurance products with different ages,different insurance periods,different gender balance premiums,but also can obtain the asset share that can be reached when the insurance policy expires.This paper is divided into six chapters.The first chapter is the introduction part,which mainly introduces the research status of life insurance pricing and introduces the application of backward stochastic differential equations in finan-cial mathematics.The second chapter mainly introduces the related backward stochastic differential equations that need to be used in this thesis and the ba-sic theoretical knowledge in life insurance pricing,and introduces the hypothesis selection in actuarial practice.In the third chapter,based on the no-arbitrage pricing thought in option pricing,the paper improved discrete backward stochas-tic differential equation model under the relevant assumptions,solves the model using Fourier transform,and gives two kinds of life insurance product equilib-rium premium solution steps.The fourth chapter focuses on the critical illness insurance and term life insurance products,and uses the third chapter backward stochastic differential equation model to give balanced premiums of different ages,genders,and different coverages,and compares them with actual insurance premi-um calculation results.Chapter 5 is a summary and outlook.The sixth chapter is the specific premium calculation results.The main innovations in this paper:1.Consider the policy asset share and survival factor attenuation when model-ing the claims process,the discrete backward stochastic differential equation model is improved,and the formula for calculating the asset share under the backward stochastic differential equation model is obtained.It is compared with the calculation formula of the asset share in the asset share pricing method,which shows that the model has operability,which provides a new idea for life insurance pricing;2.In response to the popular insurance products in the current market,name-ly,critical illness insurance and term life insurance,discrete backward s-tochastic differential equation model is used to provide balanced premiums for different ages,different insurance periods and different coverage policies through numerical experiments.Comparing with the balanced premium calculated by the actuarial theory method,the difference between the two is small,and the feasibility of the discrete backward stochastic differential equation model is illustrated from the perspective of numerical experiments.