Exit times for semimartingales under nonlinear expectation

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Liu, Guomin¹ 

[1] Fudan Univ, Sch Math Sci, Shanghai, Peoples R China

关键词: Nonlinear expectation;    G-expectation;    Multi-dimensional nonlinear semimartingales;    Exit times;    Quasi-continuity;   

DOI  :  10.1016/j.spa.2020.07.017

来源: Elsevier

【 摘 要 】

Let (E) over cap be the upper expectation of a weakly compact but possibly non-dominated family P of probability measures. Assume that Y is a d-dimensional P-semimartingale under (E) over cap. Given an open set Q subset of R-d, the exit time of Y from Q is defined by tau(Q) := inf{t >= 0 : Yt is an element of Q(c)}.( ) The main objective of this paper is to study the quasi-continuity properties of tau(Q) under the nonlinear expectation (E) over cap. Under some additional assumptions on the growth and regularity of Y, we prove that tau(Q) <^> t is quasi-continuous if Q satisfies the exterior ball condition. We also give the characterization of quasi-continuous processes and related properties on stopped processes. In particular, we obtain the quasi-continuity of exit times for multi-dimensional G-martingales, which nontrivially generalizes the previous one-dimensional result of Song (2011). (C) 2020 Elsevier B.V. All rights reserved.

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