The Representation Theorems For Generators Of BSDE Under Local Lipschitz Condition

Pardoux and Peng first solved the existence and uniqueness theorem of the Solution of the nonlinear BSDE under Lipschitz condition in 1990. From then on, many people make futher study on BSDE and its applications in mathematical finance, stochastic control, partial differential equation(PDE), stochastic differential games and economy, which develop BSDE further. Now the theory of BSDE is not only widely considered as the main tool of study financial mathematical(for example, the problem of pricing of options and derivative securities) but also the efficient tool of studying stochastic control, stochastic games, the problem of probabilistic representation of solution of nonlinear PDE and so on. The comparison theorem is one of the achievements of BSDE, there are many people have been devoted to converse comparison theorem. For studying converse comparison theorem, S.Peng established an important theorem, i.e. the representation theorems for generators of BSDE,It is am important tools For studying converse comparison theorem, so It has very important significance.This paper based on the predecessor's work, we generalize the BSDE in this paper. In chapter one we introduced the existence and uniqueness of the solution of the BSDE under local Lipschitz condition; In chapter two we introduced the comparison theorem of the BSDE under local Lipschitz condition; In chapter three we introduced the representation theorems for generators of BSDE, which is the main result of this paper.We set the following assumption to the generators g :(A1)(Local Lipschitz condition)? N>0,there exist K N> 0,when x≤N,(A3) g (t,y,z) is continuous in t∈[0,T](A4) There are two constant C>0 andα∈[0,1] make We have theorem(3.1.1) and (3.1.2) existed ,based on this we have the theorem(3.2.1)...