Stochastic Differential Equations And Its Application

The solution of a backward stochastic differential equation is a pair of process (K,Z) satisfyingwhere g is the generator, and ξ is the terminal condition.We are concerned with the properties of backward stochastic differential equations and their application to finance. These equations were first introduced by Bismut(1973) in the linear case and by Parodoux and Peng (1997)in the general case.In this article ,we give the existence and uniqueness of the solution of a kind of generalized backward stochastic differential equations, and give a kind of fuzzy measure induced by g-Expectation. At the end of the paper, we give the application of BSDE in finance.Key Words:backward stochastic differential equation;g-Expectation;Pricing g-martingale;g-supersolution;g-supermartingale;fuzzy measure;Contingent;Claim...