Stochastic differential games with state constraints and Isaacs equations with nonlinear Neumann problems

Lishun Xiao; Dejian Tian

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arXiv · 1705.04221

Stochastic differential games with state constraints and Isaacs equations with nonlinear Neumann problems

Lishun Xiao·Dejian Tian

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Abstract

We investigate a two-player zero-sum stochastic differential game problem with the state process being constrained in a connected bounded closed domain, and the cost functional described by the solution of a generalized backward stochastic differential equation (GBSDE for short). We show that the value functions enjoy a (strong) dynamic programming principle, and are the unique viscosity solution of the associated Hamilton-Jacobi-Bellman-Isaacs equations with nonlinear Neumann boundary problems. To obtain the existence for viscosity solutions, we provide a new approach utilizing the representation theorem for generators of the GBSDE, which is proved by a random time change method and is a novel result in its own right.

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BibTeX RIS

Lishun Xiao, Dejian Tian. 2017-05-11. Stochastic differential games with state constraints and Isaacs equations with nonlinear Neumann problems. https://arxiv.org/abs/1705.04221

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