A Weak Dynamic Programming Principle for Zero-Sum Stochastic Differential Games with Unbounded Controls

2012/10/10 by Bayraktar, Erhan, Yao, Song · 1 citation
#49L20 #49L25 #49N70 #91A23 #91A60 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.1210.2788

Abstract

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.

Cited by

• Turnpike properties for zero-sum stochastic linear quadratic differential games of Markovian regime switching system

Related

• On Zero-Sum Stochastic Differential Games
• Zero-sum Stochastic Differential Games of Impulse Versus Continuous Control by FBSDEs
• Zero-sum stochastic differential games of generalized McKean-Vlasov type *
• A BSDE Approach to Stochastic Differential Games Involving Impulse Controls and HJBI Equation
• On zero-sum Stochastic Differential Games with Jump-Diffusion driven\n state: A viscosity solution framework