关于g-上鞅的上穿不等式和强g-上鞅(Ⅱ)

On Upcrossing Inequality for g-Supermartingale and Strong g-Supermartingale(Ⅱ)

继续研究了g＿上鞅的收敛定理,右连续修正以及其他性质,得出g＿上鞅的右连续修正样本是强g＿上鞅。文章的讨论与结果在连续的情形已证实可应用于g＿上鞅的非线性Doob＿Meyer分解的讨论,及不完全金融市场的期权定价及经济理论的效用函数的讨论中。因此,在带跳情形,也将可有类似应用。

This paper goes on improving the Convergence Theorem,the right-continuous modification and other properties of g-martingale. It also shows that the right-continuous modification of any g-supermartingale is a strong g-supermartingale. What the paper introduced in the case of continuity has been proved that it can be applied to the discussions for g-supermartingale of the nonlinear Doob-Meyer decomposition,to the contingent claims pricing in the incomplete markets and to the utility functions in economic theory.So that it will have the same applications in the case with jumps.