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Article Dans Une Revue Mathematics of Operations Research Année : 2015

Stochastic Target Games and Dynamic Programming via Regularized Viscosity Solutions

Résumé

We study a class of stochastic target games where one player tries to find a strategy such that the state process almost-surely reaches a given target, no matter which action is chosen by the opponent. Our main result is a geometric dynamic programming principle which allows us to characterize the value function as the viscosity solution of a non-linear partial differential equation. Because abstract mea-surable selection arguments cannot be used in this context, the main obstacle is the construction of measurable almost-optimal strategies. We propose a novel approach where smooth supersolutions are used to define almost-optimal strategies of Markovian type, similarly as in ver-ification arguments for classical solutions of Hamilton–Jacobi–Bellman equations. The smooth supersolutions are constructed by an exten-sion of Krylov's method of shaken coefficients. We apply our results to a problem of option pricing under model uncertainty with different interest rates for borrowing and lending.
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Dates et versions

hal-00846830 , version 1 (21-07-2013)
hal-00846830 , version 2 (30-01-2015)

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Citer

Bruno Bouchard, Marcel Nutz. Stochastic Target Games and Dynamic Programming via Regularized Viscosity Solutions . Mathematics of Operations Research, 2015, ⟨10.1287/moor.2015.0718⟩. ⟨hal-00846830v2⟩
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