Existence And Uniqueness For Solutions Of Several Class Of BSDEs With General Time Horizons And Stochastic Conditions

In this paper, we mainly study the existence and uniqueness of solutions inL pspace forseveral class of backward stochastic differential equations (BSDE for short) with general timehorizons, which generalizes some existing results.In chapter1, we introduce the theory background of BSDEs, research contents and somepreliminaries for the following chapters. In chapter2, we obtain the existence and uniqueness ofsolutions inL pspace for one-dimensional BSDE with general time horizons whose generatorsatisfies stochastic Lipschitz conditions by using the stopping times to get a strict contraction onevery intervals on the ground of a prior estimate. This result generalizes Proposition3.2inFan(2011) and Theorem3.1in Hou(2013). In chapter3, we show a comparison theorem ofsolutions inL pspace for a class of one-dimensional BSDEs with stochastic conditions andgeneral time horizons on the ground of chapter2. This result partly generalizes Theorem2.2inFan(2011). In chapter4, we prove the existence of solutions inL pspace for one-dimensionalBSDEs with general time horizons whose generator satisfies stochastic linear-growth byconstruct a series of BSDEs whose generator satisfies stochastic Lipschitz conditions on theground of chapter2and chapter3. This result generalizes Theorem5.1in Hou(2013) and themain result in Chen(2010). In chapter5, we give a summary of this paper.