Mokobodzki’s intervals: An approach to Dynkin games when value process is not a semimartingale

Tomasz Klimsiak and Maurycy Rzymowski

Stochastic Processes and their Applications, 2026, vol. 191, issue C

Abstract: We study Dynkin games governed by a nonlinear Ef-expectation on a finite interval [0,T], with payoff càdlàg processes L,U of class (D) which are not imposed to satisfy (weak) Mokobodzki’s condition – the existence of a càdlàg semimartingale between the barriers. For that purpose we introduce the notion of Mokobodzki’s stochastic intervals ℳ(θ) (roughly speaking, maximal stochastic interval on which Mokobodzki’s condition is satisfied when starting from the stopping time θ) and the notion of reflected BSDEs without Mokobodzki’s condition. We prove an existence and uniqueness result for RBSDEs with driver f that is non-increasing with respect to the value variable (no restrictions on the growth) and Lipschitz continuous with respect to the control variable, and with data in L1 spaces. Next, we show numerous results on Dynkin games with most notable saying that the game is not played beyond ℳ(θ), when starting from θ.

Keywords: Dynkin games; Mokobodzki’s condition; BSDEs; Reflected BSDEs (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.spa.2025.104786

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