On Zero-Sum Optimal Stopping Games

Erhan Bayraktar, Zhou Zhou

    Research output: Contribution to journalArticlepeer-review

    Abstract

    On a filtered probability space (Ω,F,P,F=(Ft)t=0,…,T), we consider stopping games V¯:=infρ∈Tiisupτ∈TE[U(ρ(τ),τ)] and V̲:=supτ∈Tiinfρ∈TE[U(ρ,τ(ρ))] in discrete time, where U(s, t) is Fs t-measurable instead of Fs t-measurable as is assumed in the literature on Dynkin games, T is the set of stopping times, and Ti and Ti i are sets of mappings from T to T satisfying certain non-anticipativity conditions. We will see in an example that there is no room for stopping strategies in classical Dynkin games unlike the new stopping game we are introducing. We convert the problems into an alternative Dynkin game, and show that V¯=V̲=V, where V is the value of the Dynkin game. We also get optimal ρ∈ Ti i and τ∈ Ti for V¯ and V̲ respectively.

    Original languageEnglish (US)
    Pages (from-to)457-468
    Number of pages12
    JournalApplied Mathematics and Optimization
    Volume78
    Issue number3
    DOIs
    StatePublished - Dec 1 2018

    Bibliographical note

    Funding Information:
    This research was supported in part by the National Science Foundation under grant

    Funding Information:
    This research was supported in part by the National Science Foundation under grant DMS-1613170.

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