Discrete Backward Stochastic Equations

Considering the backward stochastic differential equations driven by a Brownian motion,When discretizing a Brownian motion with Random Walk,we can obtain a discrete backward stochastic equations driven by a discrete martingale which has the predictable representation property。So we may focus directly on a backward stochastic equations driven by a discrete martingale which has the predictable representation property。Chapter 2 states that this kind of discrete martingale which has the predictable representation property is common by introducing the (B,S) model of no-arbitrage market and classical betting a unbias coin strategy,that is,the existence of this kind of backward stochastic equations is certain。Chapter 3 defines the existence and uniqueness of the solution of this kind of BSEs and gives the existence and uniqueness results of the solution under Lipschitz condition。Moreover,continuous dependence property,comparison theorem in one dimension , forward-backward stochastic equations (FBSEs) and g-expectation are discussed。For the last chapter,traditional pricing method of contingent claim in no-arbitrage (B,S) market is fistly introduced,and then,pricing method of g-expectation of BSE is given,from comparison we can see that all its need for pricing method of BSE is to make a Girsanov's transformation of martingale,without constructing a self-financing portfolio,which is indispensable in traditional pricing method and always proved to be troublesome。In the discrete framework,many numerical solution can be conveniently done by computer。At the end of the essay,pricing formula of Forward and European call option are deduced in the discrete framework。...