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Dynkin games with heterogeneous beliefs

Part of: Stochastic processes Mathematical finance

Published online by Cambridge University Press:  04 April 2017

Erik Ekström ,
Kristoffer Glover  and
Marta Leniec
Erik Ekström*
Affiliation:
Uppsala University
Kristoffer Glover*
Affiliation:
University of Technology Sydney
Marta Leniec*
Affiliation:
Uppsala University
*
* Postal address: Department of Mathematics, Uppsala University, Box 480, 75106 Uppsala, Sweden.
** Postal address: University of Technology Sydney, PO Box 123, Broadway, NSW 2007, Australia.
* Postal address: Department of Mathematics, Uppsala University, Box 480, 75106 Uppsala, Sweden.
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Abstract

We study zero-sum optimal stopping games (Dynkin games) between two players who disagree about the underlying model. In a Markovian setting, a verification result is established showing that if a pair of functions can be found that satisfies some natural conditions then a Nash equilibrium of stopping times is obtained, with the given functions as the corresponding value functions. In general, however, there is no uniqueness of Nash equilibria, and different equilibria give rise to different value functions. As an example, we provide a thorough study of the game version of the American call option under heterogeneous beliefs. Finally, we also study equilibria in randomized stopping times.

Keywords

Dynkin gameheterogeneous beliefmultiple Nash equilibriaoptimal stopping theory

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 91G20: Derivative securities
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 1 , March 2017 , pp. 236 - 251
Copyright
Copyright © Applied Probability Trust 2017 

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