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Solving finite time horizon Dynkin games by optimal switching

Part of: Stochastic processes Mathematical finance Game theory

Published online by Cambridge University Press:  09 December 2016

Randall Martyr
Randall Martyr*
Affiliation:
The University of Manchester
*
* Current address: School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK. Email address: r.martyr@qmul.ac.uk
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Abstract

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This paper uses recent results on continuous-time finite-horizon optimal switching problems with negative switching costs to prove the existence of a saddle point in an optimal stopping (Dynkin) game. Sufficient conditions for the game's value to be continuous with respect to the time horizon are obtained using recent results on norm estimates for doubly reflected backward stochastic differential equations. This theory is then demonstrated numerically for the special cases of cancellable call and put options in a Black‒Scholes market.

Keywords

Optimal stopping gameNash equilibriumsaddle pointoptimal stoppingSnell envelopeoptimal switching

MSC classification

Primary: 91A55: Games of timing
Secondary: 91A05: 2-person games 60G40: Stopping times; optimal stopping problems; gambling theory 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 4 , December 2016 , pp. 957 - 973
Copyright
Copyright © Applied Probability Trust 2016 

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