g-期望的凸性及其应用

Convexity of g-expectations and its application

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.