A WEAK DYNAMIC PROGRAMMING PRINCIPLE FOR ZERO-SUM STOCHASTIC DIFFERENTIAL GAMES WITH UNBOUNDED CONTROLS

作者：Bayraktar Erhan^*; Yao Song

来源：SIAM Journal on Control and Optimization, 2013, 51(3): 2036-2080.

DOI：10.1137/120897638

• zero-sum stochastic differential games
• Elliott-Kalton strategies
• weak dynamic programming principle
• backward stochastic differential equations
• viscosity solutions
• fully nonlinear PDEs

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 nonlinear partial differential equation in the viscosity sense.

• 出版日期2013