A Density Result Of Backward Stochastic Differential Equation

The general theory of backward stochastic differential equations (BSDE) has only recently developed. The nonlinear case began early in 1990s. Peng and Pardoux introduced a general form of BSDE under the Lipschitz condition and proved the existence and uniqueness of the solution to BSDE driven by the Brown motion adapted to the natural flow generated by Brown motion. After years the theory of BSDE has further development, widely used in many areas of mathematics and has become an important tool, for example, mathematical finance, stochastic optimal control policy and partial differential equations.On BSDE itself, under the situation with the Lipschitz coefficient there is much systematic study and the results are perfect. Under Lipschitz condition , it seems not much study. We give a density result of the solution to BSDE under non-Lipschitz coefficient with Mao Xuerong'condition.This result promots that of TangQi's.Chapter 3 introduces a class of stochastic differential utility of BSDE which are founded by famous economist Duffle and Epstein. wo gave out the nature of the stochastic differential utility, including "risk aversion", the course of consumption, consumptoin utility.and so on the nature of consumer preferences;The section II introduces the Black-Schloesformula which is drived by BSDE.