Pricing Life Insurance Product Under Jump-diffusion Term Structure Model

This thesis constructs a zero-coupon bond pricing model within the framework of the stochastic forward rate with jump.Based on this research we address the pricing of longevity bonds and unit-linked pure endowment insurance,and local risk minimization hedging method.In this thesis,a zero-coupon bond pricing formula is derived within the framework of a stochastic forward rate term structure model with jump.Then for longevity bonds with the insured’s survival at maturity as the payout condition,the product of the zero-coupon bond price and the survival probability under the forward probability measure?Q,which is denominated in units of zero-coupon bond price,is obtained using the measure-transformed Bayesian formula under the stochastic mortality intensity assumption.Unit-linked pure endowment insurance is conditional on the survival of the insured,and the benefit payment at maturity is related to the investment return in the financial market.In this thesis,we construct a combined financial-insurance incomplete market with bank account,zero-coupon bond,stock,and mortality intensity as deterministic functions,and solve the prob-lem of pricing and local risk minimization hedging for unit-linked pure endowment insurance in this combined market.In the combined financial-insurance market,we assume that the price processes of two risky assets,zero-coupon bond and stock,are driven by two independent stan-dard Brownian motions and the same Poisson stochastic measure,and that the financial and insurance markets are independent.First,we prove the existence of the minimum martingale measureˉQ~*and give its explicit form with the help of Radon-Nikodym derivative with respect to the objective probability measureˉP.Also,using Girsanov’s transformation theorem,we give the stochastic differential equations satisfied by the zero-coupon bond and stock discounted price processes under the minimum martingale measureˉQ~*.Second,using the no-arbitrage pricing theory,we give the no-arbitrage price equation for unit-linked pure endowment insur-ance under the minimum martingale measureˉQ~*and derive the differential expression for its discounted price process under the minimum martingale measureˉQ~*.Further,we show that the above discounted price process can be decomposed into the sum of a stochastic integral over the discounted price process of the risky assets andˉP-martingale{L_t},which is orthogonal to the local martingale part of the discounted price process of the risky assets.Based on this decom-position of the discounted price process of unit-linked pure endowment insurance,we construct a portfolio trading strategy to hedge the contingent claim of unit-linked pure endowment insur-ance and further verify that this trading strategy is a local risk minimization hedging strategy for the contingent claim of unit-linked pure endowment insurance.Finally,numerical experiments are conducted on the local risk minimization hedging strategy using the Monte Carlo method.Results show that the hedging strategy for zero-coupon bond is more sensitive to the volatile situation of asset prices in the financial market,but the hedging strategy for stock is less affected by it.