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

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  • Klimsiak, Tomasz
  • Rzymowski, Maurycy

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.

Suggested Citation

  • Klimsiak, Tomasz & Rzymowski, Maurycy, 2026. "Mokobodzki’s intervals: An approach to Dynkin games when value process is not a semimartingale," Stochastic Processes and their Applications, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:spapps:v:191:y:2026:i:c:s0304414925002303
    DOI: 10.1016/j.spa.2025.104786
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    References listed on IDEAS

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    1. Touzi, N. & Vieille, N., 1999. "Continuous-Time Dynkin Games with Mixed Strategies," Papiers d'Economie Mathématique et Applications 1999.112, Université Panthéon-Sorbonne (Paris 1).
    2. Klimsiak, Tomasz, 2021. "Non-semimartingale solutions of reflected BSDEs and applications to Dynkin games," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 208-239.
    3. Bayraktar, Erhan & Yao, Song, 2015. "Doubly reflected BSDEs with integrable parameters and related Dynkin games," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4489-4542.
    4. Briand, Ph. & Delyon, B. & Hu, Y. & Pardoux, E. & Stoica, L., 2003. "Lp solutions of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 109-129, November.
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