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April 2016 Stochastic Perron for stochastic target games
Erhan Bayraktar, Jiaqi Li
Ann. Appl. Probab. 26(2): 1082-1110 (April 2016). DOI: 10.1214/15-AAP1112


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.


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Erhan Bayraktar. Jiaqi Li. "Stochastic Perron for stochastic target games." Ann. Appl. Probab. 26 (2) 1082 - 1110, April 2016.


Received: 1 September 2014; Revised: 1 January 2015; Published: April 2016
First available in Project Euclid: 22 March 2016

zbMATH: 1337.93100
MathSciNet: MR3476633
Digital Object Identifier: 10.1214/15-AAP1112

Primary: 49L20 , 49L25 , 60G46 , 93E20
Secondary: 35D05 , 60H30 , 91B28

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

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.26 • No. 2 • April 2016
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