The Annals of Applied Probability

Stochastic Perron for stochastic target games

Erhan Bayraktar and Jiaqi Li

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Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 26, Number 2 (2016), 1082-1110.

Dates
Received: September 2014
Revised: January 2015
First available in Project Euclid: 22 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1458651828

Digital Object Identifier
doi:10.1214/15-AAP1112

Mathematical Reviews number (MathSciNet)
MR3476633

Zentralblatt MATH identifier
1337.93100

Subjects
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

Keywords
The stochastic target problem stochastic Perron method viscosity solutions geometric dynamic programming principle

Citation

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


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References

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