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Convexity and sublinearity of g-expectations
Statistics & Probability Letters ( IF 0.9 ) Pub Date : 2022-06-09 , DOI: 10.1016/j.spl.2022.109569
Ronglin Ji , Xuejun Shi , Shijie Wang , Jinming Zhou

Under the basic assumptions of g-expectations defined in Chen and Wang (2000), we establish the one-to-one correspondence between generators of backward stochastic differential equations (BSDEs for short) and the convexity (resp. conditional convexity, Ft-convexity) of g-expectations, respectively. We also obtain the relationship between generators of BSDEs and the sublinearity (resp. conditional sublinearity, Ft-sublinearity) of g-expectations, respectively. Moreover, we provide the reasonable assumptions on generators of BSDEs for the further study on dynamic risk measures by applying the theory of g-expectations.



中文翻译:

g - 期望的凸性和次线性

在基本假设下 G-在 Chen 和 Wang (2000) 中定义的期望,我们建立了后向随机微分方程(简称 BSDE)和凸性(分别是条件凸性, F-凸性)的 G-期望,分别。我们还获得了 BSDE 的生成器与次线性(分别是条件次线性, F-次线性)的 G-期望,分别。此外,我们通过应用理论,为进一步研究动态风险度量提供了关于 BSDE 生成器的合理假设。 G-期望。

更新日期:2022-06-09
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