On the Robust Dynkin Game

32 Pages Posted: 21 Jul 2016  

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Song Yao

University of Pittsburgh

Date Written: June 30, 2015

Abstract

We analyze a robust version of the Dynkin game over a set P of mutually singular probabilities. We first prove that conservative player's lower and upper value coincide (Let us denote the value by $V$). Such a result connects the robust Dynkin game with second-order doubly reflected backward stochastic differential equations. Also, we show that the value process $V$ is a submartingale under an appropriately defined nonlinear expectation up to the first time when $V$ meets the lower payoff process. If the probability set P is weakly compact, one can even find an optimal triplet for the value V0. The mutual singularity of probabilities in P causes major technical difficulties. To deal with them, we use some new methods including two approximations with respect to the set of stopping times.

Keywords: robust Dynkin game, nonlinear expectation, dynamic programming principle, controls in weak formulation, weak stability under pasting, martingale approach, path-dependent stochastic di erential equations with controls, optimal triplet, optimal stopping with random maturity

Suggested Citation

Bayraktar, Erhan and Yao, Song, On the Robust Dynkin Game (June 30, 2015). Available at SSRN: https://ssrn.com/abstract=2806552

Erhan Bayraktar (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Song Yao

University of Pittsburgh ( email )

507 Thackeray Hall
Pittsburgh, PA 15260
United States

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