Research On The Pricing Of The Unit-linked Insurance Based On The Model Of Backward Stochastic Differential Equation

In this dissertation，we mainly investigate net premiums, periodic premiums and unearnedpremium reserve of two kinds of pure unit-linked insurances and unit-linked insurances underguarantee based on the model of Backward Stochastic Differential Equation(BSDE). And thenwe proof integral-partial equations of the unearned premium reserve.In the first chapter, we outline the background and the major work.In the second chapter, we state the theoretical knowledge related with the dissertation,including theorem of BSDE and stochastic analysis.In the third chapter, we give two models: Actuarial market and finance market. Under thecondition of complete market, we derive the contingent claim formula using the theory of BSDE.In the fourth chapter, based on the independent of Actuarial market and finance marketassumption, we derive the net premiums of the unit-linked endowment insurance and terminsurance, the net premiums of the unit-linked endowment insurance and term insurance underguarantee.In the fifth chapter, we give pricing formula of periodic premium and unearned premiumreserve. And then we proof integral-partial equations of the unearned premium reserve.In the sixth chapter, we summarize the main result of the dissertation and point out theweakness of this dissertation and some issues remaining unsolved, and then net premium ofunit-linked insurances under guarantee was simulated.