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International conference "Stochastic Optimization and Optimal Stopping"
September 25, 2012 12:10, Moscow, Steklov Mathematical Institute of RAS
 

Plenary talks


Stochastic Perron's method and verification without smoothness using viscosity comparison: obstacle problems and Dynkin games

Erhan Bayraktar

University of Michigan
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Erhan Bayraktar
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Abstract: We adapt the Stochastic Perron's method in Bayraktar and Sirbu (arXiv:1103.0538) to the case of double obstacle problems associated to Dynkin games. We construct, symmetrically, a viscosity sub-solution which dominates the upper value of the game and a viscosity super-solution lying below the lower value of the game. If the double obstacle problem satisfies the viscosity comparison property, then the game has a value which is equal to the unique and continuous viscosity solution. In addition, the optimal strategies of the two players are equal to the first hitting times of the two stopping regions, as expected. The (single) obstacle problem associated to optimal stopping can be viewed as a very particular case. This is the first instance of a non-linear problem where the Stochastic Perron's method can be applied successfully.

Language: English

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