Stochastic Target Games with Controlled Loss

Bouchard, Bruno; Moreau, Ludovic; Nutz, Marcel

Bouchard, Bruno; Moreau, Ludovic; Nutz, Marcel (2014), Stochastic Target Games with Controlled Loss, The Annals of Applied Probability, 24, 3, p. 899-934. http://dx.doi.org/10.1214/13-AAP938

Type

Article accepté pour publication ou publié

Date

2014

Journal name

The Annals of Applied Probability

Volume

Number

Publisher

Institute of Mathematical Statistics

Pages

899-934

Abstract (EN)

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 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.

Subjects / Keywords

Geometric dynamic programming principle; Viscosity solution; Stochastic target; Stochastic game