Variational Inequalities on Unbounded Domains for Zero-Sum Singular Controller vs. Stopper Games

被引：0

作者：

Bovo A. ^{[1
]}

De Angelis T. ^{[1
,2
]}

Issoglio E. ^{[3
]}

机构：

[1] Department of Economics Social Studies Applied Mathematics and Statistics, School of Management and Economics, University of Torino, Torino

[2] Collegio Carlo Alberto, Torino

[3] Department of Mathematics "G. Peano", University of Torino, Torino

来源：

Mathematics of Operations Research | 2024年 / 1卷

关键词：

controlled diffusions; gradient constraints; obstacle problems; optimal stopping; penalization methods; singular control; unbounded domains; variational inequalities; zero-sum stochastic games;

D O I：

10.1287/moor.2023.0029

中图分类号：

学科分类号：

摘要：

We study a class of zero-sum games between a singular controller and a stopper over a finite-time horizon. The underlying process is a multidimensional (locally nondegenerate) controlled stochastic differential equation (SDE) evolving in an unbounded domain. We prove that such games admit a value and provide an optimal strategy for the stopper. The value of the game is shown to be the maximal solution in a suitable Sobolev class of a variational inequality of min-max type with an obstacle constraint and a gradient constraint. Although the variational inequality and the game are solved on an unbounded domain, we do not require boundedness of either the coefficients of the controlled SDE or of the cost functions in the game. © 2024 INFORMS.

引用

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