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A probabilistic verification theorem for the finite horizon two-player zero-sum optimal switching game in continuous time

Part of: Game theory Miscellaneous topics in calculus of variations and optimal control Stochastic processes

Published online by Cambridge University Press:  07 August 2019

S. Hamadène ,
R. Martyr  and
J. Moriarty
S. Hamadène*
Affiliation:
Le Mans Université
R. Martyr*
Affiliation:
Le Mans Université
J. Moriarty*
Affiliation:
Queen Mary University of London
*
*Postal address: Le Mans Université, Avenue Olivier Messiaen, 72085 Le Mans, Cedex 9, France. Email address: [email protected]
**Postal address: School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK.
**Postal address: School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK.
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Abstract

In this paper we study continuous-time two-player zero-sum optimal switching games on a finite horizon. Using the theory of doubly reflected backward stochastic differential equations with interconnected barriers, we show that this game has a value and an equilibrium in the players’ switching controls.

Keywords

Optimal switchingoptimal switching gamestopping timeoptimal stopping problemoptimal stopping gamebackward stochastic differential equation

MSC classification

Primary: 91A55: Games of timing
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory 91A05: 2-person games 49N25: Impulsive optimal control problems
Type
Original Article
Information
Advances in Applied Probability , Volume 51 , Issue 2 , June 2019 , pp. 425 - 442
Copyright
© Applied Probability Trust 2019 

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