关键词: 倒向随机微分方程, g-期望, 条件g-期望, g-方差, 条件g-方差

Abstract:

A conditional variance for g-expectation, named conditional g-variance, is introduced in this paper. The uniqueness theorem for conditional g-variance is proved and the comparison theorem does not hold any more. The sufficient and necessary condition of the property of continuity of conditional g-variance depending on parameters is obtained. At last, we extend conditional g-variance from L⁴(Ω,F_T,P) to L²(Ω,F_T,μ) as a continuous mapping in H_F¹(0,T; R).

Key words: Backward stochastic differential equations, g-Expectation, Conditional g-exp-ectation, g-Variance, Conditional g-variance