g-期望关于凸(凹)函数的Jensen不等式

在文[8]的基础上和彭实戈提出的关于g-期望的最基本的条件下,证明了g-期望关于凸(凹)函数的Jensen不等式在一般意义下成立当且仅当g是关于(y,z)的超齐次(次齐次)生成元且不依赖于y．     

条件g-期望的矩不等式

找到了几个使条件g-期望的矩不等式在一般意义下成立的关于g和g-期望的充分条件.     

g-variance

In this paper, we introduce the notion of g-variance and study some properties of this operator. We find the nonlinear variance operator, g-variance, does not preserve some basic properties of traditional mathematic variance. We also consider the relationship Dμ[ξ] and supQe T^1 VarQ[ξ] （D-μ [ξ] and infQe T^1 VarQ [ξ]）. The result shows that the maximum （minimum） variance is not always equal to Dμ[·] （D-μ[·]）. If g satisfies some restrictive conditions, we get the uniqueness theorem and the comparison theorem via g-variance.     

The S-Related Dynamic Convex Valuation in the Brownian Motion Setting

Let be an array of row-wise exchangeable random elements in a separable Banach space. Strong laws of large numbers are obtained for under certain moment conditions on the random variables and a condition relating to nonorthogonality. By using reverse martingale techniques, similar results are obtained for triangular arrays of random elements inseparable Banach spaces which are row-wise exchangeable     

Jensen's Inequality for Backward Stochastic Differential Equations

Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen's inequality holds for backward stochastic differential equations with generator g if and only if g is independent of y, g(t, 0) = 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen's inequality for g-expectation in [4, 7-9].