Existence,uniqueness and comparison results for BSDEs with Levy jumps in an extended monotonic generator setting  

作　　者：Christel Geiss Alexander Steinicke 

机构地区：[1]University of Jyvaskyla,Department of Mathematics and Statistics,P.O.Box 35,40014 Jyvaskyla,Finland [2]Department of Mathematics and Information Technology,Montanuniversitaet Leoben,Leoben,Austria

出　　处：《Probability, Uncertainty and Quantitative Risk》2018年第1期253-285,共33页概率、不确定性与定量风险（英文）

基　　金：Large parts of this article were written when Alexander Steinicke was member of the Institute of Mathematics and Scientific Computing,University of Graz,Austria,and supported by the Austrian Science Fund(FWF):Project F5508-N26,which is part of the Special Research Program"Quasi-Monte Carlo Methods:Theory and Applications."。

摘　　要：We show that the comparison results for a backward SDE with jumps established in Royer(Stoch.Process.Appl 116:1358–1376,2006)and Yin and Mao(J.Math.Anal.Appl 346:345–358,2008)hold under more simplified conditions.Moreover,we prove existence and uniqueness allowing the coefficients in the linear growth-and monotonicity-condition for the generator to be random and time-dependent.In the L2-case with linear growth,this also generalizes the results of Kruse and Popier(Stochastics 88:491–539,2016).For the proof of the comparison result,we introduce an approximation technique:Given a BSDE driven by Brownian motion and Poisson random measure,we approximate it by BSDEs where the Poisson random measure admits only jumps of size larger than 1/n.

关 键 词：Backward stochastic differential equation Levy process´ comparison theorem existence and uniqueness 

分 类 号：O17[理学—数学]