A Weak Dynamic Programming Principle for Zero-Sum Stochastic Differential Games with Unbounded Controls
SIAM Journal on Control and Optimization, 51 (3), 2036-2080, 2013
42 Pages Posted: 15 Feb 2014 Last revised: 10 Jul 2016
Date Written: March 13, 2013
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.
Keywords: Zero-sum stochastic differential games, Elliott-Kalton strategies, weak dynamic programming principle, backward stochastic differential equations, viscosity solutions, fully non-linear PDEs.
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