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

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Song Yao

University of Pittsburgh

Date Written: March 13, 2013

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.

Keywords: Zero-sum stochastic differential games, Elliott-Kalton strategies, weak dynamic programming principle, backward stochastic differential equations, viscosity solutions, fully non-linear PDEs.

Suggested Citation

Bayraktar, Erhan and Yao, Song, A Weak Dynamic Programming Principle for Zero-Sum Stochastic Differential Games with Unbounded Controls (March 13, 2013). SIAM Journal on Control and Optimization, 51 (3), 2036-2080, 2013. Available at SSRN: https://ssrn.com/abstract=2395451

Erhan Bayraktar (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Song Yao

University of Pittsburgh ( email )

507 Thackeray Hall
Pittsburgh, PA 15260
United States

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