A Weak Dynamic Programming Principle for Zero-Sum Stochastic Differential Games with Unbounded Controls
Probability
2013-03-14 v2 Analysis of PDEs
Optimization and Control
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.
Cite
@article{arxiv.1210.2788,
title = {A Weak Dynamic Programming Principle for Zero-Sum Stochastic Differential Games with Unbounded Controls},
author = {Erhan Bayraktar and Song Yao},
journal= {arXiv preprint arXiv:1210.2788},
year = {2013}
}
Comments
Key words: Zero-sum stochastic differential games, Elliott-Kalton strategies, weak dynamic programming principle, backward stochastic differential equations, viscosity solutions, fully non-linear PDEs. A shorter version is to appear in the SIAM Journal on Control and Optimization