Exit times for semimartingales under nonlinear expectation

Guomin Liu

Stochastic Processes and their Applications, 2020, vol. 130, issue 12, 7338-7362

Abstract: Let Eˆ 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 Eˆ. Given an open set Q⊂Rd, the exit time of Y from Q is defined by τQ≔inf{t≥0:Yt∈Qc}.The main objective of this paper is to study the quasi-continuity properties of τQ under the nonlinear expectation Eˆ. Under some additional assumptions on the growth and regularity of Y, we prove that τQ∧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).

Keywords: Nonlinear expectation; G-expectation; Multi-dimensional nonlinear semimartingales; Exit times; Quasi-continuity (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2020.07.017

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