g-期望的凸性及其应用  

Convexity of g-expectations and its application

作　　者：纪荣林 周津名 JI Ronglin;ZHOU Jinming(School of Mathematical Sciences,Anhui University,Hefei 230601,China;School of Mathematics and Statistics,Hefei Normal University,Hefei 230601,China)

机构地区：[1]安徽大学数学科学学院,安徽合肥230601 [2]合肥师范学院数学与统计学院,安徽合肥230601

出　　处：《中山大学学报（自然科学版）》2018年第5期127-131,共5页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：江苏省自然科学基金青年基金(BK20150167);安徽大学博士科研启动经费(J01003202);安徽省高校自然科学研究(KJ2018A0496)

摘　　要：在倒向随机微分方程生成元满足基本假设的前提下,证明了g-期望的凸性、条件凸性与倒向随机微分方程生成元函数g之间的一一对应关系,从而在g-期望的框架下说明了Detlefsen-Scandolo (2005)与Jiang(2008)中关于动态凸风险度量的两种定义方式是一致的。进一步地,获得了一类时间相容的动态凸风险度量与g-期望凸性之间的对应关系。Under the basic assumptions on generators,the one-to-one correspondence between convexity and conditional convexity of g-expectations and generators of backward stochastic differential equations is obtained.Thus it is proved that the definitions of dynamic convex risk measures in Detlefsen-Scandolo(2005)and Jiang(2008)are completely same under the framework of g-expectations.Moreover,the one-to-one relation between time consistent dynamic convex risk measures via g-expectations and convexity of g-expectations is also established.

关 键 词：倒向随机微分方程 G-期望 条件凸性 动态凸风险度量 

分 类 号：O211.67[理学—概率论与数理统计]