g-期望的一些性质及其应用研究

Some Properties of g-expectations and their Applications

在经典的g-期望理论的基本假设条件下,对定义在L^(p)(1<p≤+∞)空间中的g-期望的凸性、条件凸性和F_(1)-凸性进行了研究,建立了这些性质与倒向随机微分方程的生成元函数之间的本质联系.进一步地,获得了g-期望理论与其诱导的动态(静态)凸风险度量之间的内在联系.

Under the basic assumptions of classic g-expectations,the convexity,conditional convexity and F_(1)-convexity for g-expectations in L^(p) space (1<p≤+∞)are studied,and is established the relationship between the generators of backward stochastic differential equations(BSDEs for short)and these properties of g-expectations.Furthermore,the correspondence between the theory of g-expectations and the dynamic(resp.static)convex risk measures induced by g-expectations are obtained.