A Weak Dynamic Programming Principle for Zero-Sum Stochastic   Differential Games with Unbounded Controls
  We analyze a zero-sum stochastic differential game between two competing players who can choose unbounded controls. The payoffs of the game are defined through backward stochastic differential equations. We prove that each player's priority value satisfies a weak dynamic programming principle and thus solves the associated fully non-linear partial differential equation in the viscosity sense. 
Erhan Bayraktar, Song Yao
math.PR math.AP math.OC