Pricing European Contigent Claims Under Stochastic Life

The dissertation is intended to study option pricing problems, so as to establish the mathematical model of option pricing under stochastic life by means of martingale theory, and we deduce the option pricing equation.This dissertation is divided into five chapters.The chapter 1 is preface, which summarizes the significance origin of finance mathematics, then issues some foundations and some properties of option.The European contingent claim pricing is analyzed in the second part on the condition of loan interest rate higher than the deposit one together with both stochastic, we do research on some kinds of European options under stochastic life, such as, call option, put option, pension contract, insurance contract, stock option, forward contract, and we get the fair pricing equation at time t.In the third part, under hypothesis of exponential O-U model and constant interest rate or continuous interest or incontinuous interest using martingale method ,we obtain the option pricing equation with stochastic life.In the forth part, under the hypothesis of stock price submitting to jump-diffusion process model, we gets its the option pricing equation with stochastic life by using of the martingale approach.In the last part of this thesis we discuss the multidimensional Black-Scholes pricing model under stochastic interest with stochastic life, and we gets its the option pricing equation with stochastic life by using of the martingale approach.