The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 26, Number 2 (2016), 1082-1110.
Stochastic Perron for stochastic target games
We extend the stochastic Perron method to analyze the framework of stochastic target games, in which one player tries to find a strategy such that the state process almost surely reaches a given target no matter which action is chosen by the other player. Within this framework, our method produces a viscosity sub-solution (super-solution) of a Hamilton–Jacobi–Bellman (HJB) equation. We then characterize the value function as a viscosity solution to the HJB equation using a comparison result and a byproduct to obtain the dynamic programming principle.
Ann. Appl. Probab., Volume 26, Number 2 (2016), 1082-1110.
Received: September 2014
Revised: January 2015
First available in Project Euclid: 22 March 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 93E20: Optimal stochastic control 49L20: Dynamic programming method 49L25: Viscosity solutions 60G46: Martingales and classical analysis
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.) 91B28 35D05
Bayraktar, Erhan; Li, Jiaqi. Stochastic Perron for stochastic target games. Ann. Appl. Probab. 26 (2016), no. 2, 1082--1110. doi:10.1214/15-AAP1112. https://projecteuclid.org/euclid.aoap/1458651828