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In Chapter 1，a brief history review of financial derivatives is given.Since BSDEs play a important role in mathematical finance，some pricing model are given in BSDEs.
In Chapter 2，The correspondence between BSDE and a kind of quasi-linear 2-order parabolic PDE，i.e.the”nonlinear Feynman-Kac formula” is introduced. this formula is given in[Peng(1991)]，thus the BSDE problem and PDE problem can be transformed into each other．
In Chapter 3，Some pricing method for financial derivatives are given, such as binomial method，Monte Carlo method and some PDE method.
In Chapter 4 of my doctoral thesis，I studied finite volume numerical simulation method of pricing for American option. For American option under stochastic volatility, a new kind of 9-point finite volume scheme is proposed，in which using a new technique for the 2-order hybrid cross derivatives，and upwind method for the convection item [Liang & Zhao(1997)]Key words：Backward stochastic differential equations，partial differential equations,option pricing，Feynman-Kac formula，finite Volume method；alternating-direction implicit method