Research On Backward Stochastic Differential Equations With Continuous Coefficient And Their Applications

Backward stochastic differential equations in theory and application has become a hot researchsubject in recent decades. Backward stochastic differential equations are the combination ofbackward and stochastic differential equations. Backward means that definite conditions aregiven in the end of time rather than initial time. By studying the problem of stochastic optimalcontrol, Bismut proposed the adopted solution of backward stochastic differential equations,which opens a new field of the backward stochastic differential equations. Since Peng Shige andPardoux gave the existence and uniqueness of solution for backward stochastic differentialequations, the backward stochastic differential equations has won a rapid development in theoryand application.The thesis studies the properties and theorem of reflected backward stochastic differentialequations based on the continuous coefficient of backward stochastic differential equations.According to the adopted solution of backward stochastic differential equations under the certainconditions, the adopted solution of reflected backward stochastic differential equations wasobtained where the coefficient is continuous, having a linear growth, and the terminal conditionis squared integrable. Then, some useful conclusions were got in the field where some theoremand properties of backward stochastic differential equations were applied to the reflectedbackward stochastic differential equations.Insurance pricing, the core of insurance actuarial, was discussed based on using the backwardstochastic differential equations and the insurance investment theory. Considering the neutral riskof insurance for companies, the optimization problem of insurance companies for premium wasdiscussed. Given a risk-free assets and two risky assets in financial market, we derive theinsurance pricing formula based on the investment theory by establishing the forward-backwardstochastic differential equations for insurance pricing problem, which can help insurancecompanies to make a reasonable premium price, improving the strength of insurer and marketcompetitiveness. Finally, the pricing problem of the option were given and explored by takingEuropean call option as an example, we derived the classic Black-Scholes model based on thetheory of backward stochastic differential equations.