Representation theorem and viability property for multidimensional BSDEs and their applications  

作　　者：Xuejun Shi Long Jiang 

机构地区：[1]School of Mathematics and Statistics,Shandong Normal University,Jinan 250358,China [2]School of Mathematics,China University of Mining and Technology,Xuzhou 221116,China

出　　处：《Probability, Uncertainty and Quantitative Risk》2023年第3期373-390,共18页概率、不确定性与定量风险（英文）

基　　金：supported by the Natural Science Foundation of Shandong Province(Grant Nos.ZR2022MA079,ZR2021MG049);the National Social Science Funding of China(Grant No.21CJY027).

摘　　要：The representation theorem and the viability property for backward stochastic differential equations(BSDEs)require further exploration,given their widespread use in both theory and practical applications.In this study,we present a positive answer to the long-standing open question of whether the representation theorem still holds in the L^(2)-sense under the standard assumptions of square integrability and Lipschitzian continuity on the generators of BSDEs.In the process,the multidimensional case is considered.Subsequently,based on the representation theorem,we obtain a necessary and sufficient condition for the viability property of the BSDEs under standard conditions on the generators.This removes the requirement for the generator to possess the properties of stronger integrability and continuity with respect to time variables.As an application of these results,we conduct various types of comparisons and converse comparisons for the solutions of multidimensional BSDEs,and several properties of the multidimensional g-expectation are obtained.

关 键 词：Backward stochastic differential equation Viability property Representation theorem Comparison theorem 

分 类 号：O21[理学—概率论与数理统计]