Faculty Publications

Sub-Value and Sup-Value of a Linear Diffusion Game

Document Type

Article

Keywords

Bellman–Isaacs equations, linear diffusion process, Stochastic differential game, sub-value, sup-value

Journal/Book/Conference Title

Advances in Applied Probability

First Page

1

Last Page

48

Abstract

In this paper, we solve an exit probability game between two players, each of whom controls a linear diffusion process. One player controls its process to minimize the probability that the difference of the processes reaches a low level before it reaches a high level, while the other player aims to maximize the probability. By solving the Bellman–Isaacs equations, we find the sub-value and sup-value functions of the game in explicit forms, which are twice continuously differentiable. The optimal plays associated with the sub-value and sup-value are also found explicitly.

Department

Department of Mathematics

Original Publication Date

1-21-2026

DOI of published version

10.1017/apr.2025.10047

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