Stochastic target games with controlled loss
  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. 
Bruno Bouchard, Ludovic Moreau, Marcel Nutz
math.OC math.PR q-fin.PR