The Annals of Applied Probability

Stochastic target games with controlled loss

Bruno Bouchard, Ludovic Moreau, and Marcel Nutz

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We study a stochastic game where one player tries to find a strategy such that the state process reaches a target of controlled-loss-type, no matter which action is chosen by the other player. We provide, in a general setup, a relaxed geometric dynamic programming principle for this problem and derive, for the case of a controlled SDE, the corresponding dynamic programming equation in the sense of viscosity solutions. As an example, we consider a problem of partial hedging under Knightian uncertainty.

Article information

Ann. Appl. Probab. Volume 24, Number 3 (2014), 899-934.

First available in Project Euclid: 23 April 2014

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Zentralblatt MATH identifier

Primary: 49N70: Differential games 91A23: Differential games [See also 49N70] 91A60: Probabilistic games; gambling [See also 60G40] 49L20: Dynamic programming method 49L25: Viscosity solutions

Stochastic target stochastic game geometric dynamic programming principle viscosity solution


Bouchard, Bruno; Moreau, Ludovic; Nutz, Marcel. Stochastic target games with controlled loss. Ann. Appl. Probab. 24 (2014), no. 3, 899--934. doi:10.1214/13-AAP938.

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