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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.

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.

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

Solving finite time horizon Dynkin games by optimal switching

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2 results

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

Solving finite time horizon Dynkin games by optimal switching