文章基本信息

标题：A Doob-Meyer decomposition under model ambiguity: the case of compactness
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作者：Erick Treviño-Aguilar
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2021
卷号：18
期号：1
页码：617
DOI：10.30757/ALEA.v18-24
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We consider families of equivalent probability measures Q with a property related to concepts known in the literature under different names such as rectangularity or multiplicative stability. For the problems considered in this paper such a property yields dynamical consistency. We prove under a weak-compactness assumption with general filtrations and continuous processes that all semimartingales have an additive decomposition as the sum of a predictable non-decreasing process and a universal local supermartingale, by this concept we mean a process that is a local supermartingale with respect to each element of Q. We also show that processes having a supermartingale property with respect to a superadditive nonlinear conditional expectation associated to the family Q are always semimartingales under weak-compactness. These results are relevant in stochastic optimization problems including optimal stopping under model ambiguity.
其他关键词：Doob-Meyer Decomposition, Model ambiguity, Optimal stopping, Supermartingales, Semimartingales.