Stochastic target games with controlled loss

Abstract

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.

Published in at http://dx.doi.org/10.1214/13-AAP938 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Weak Dynamic Programming for Generalized State Constraints
• Optimal arbitrage under model uncertainty
• On Zero-Sum Stochastic Differential Games

Cited by in corpus (2)

• Arbitrage and duality in nondominated discrete-time models
• Stochastic Perron for stochastic target games