Variational inequalities on unbounded domains for zero-sum singular-controller vs. stopper games

Autor:	Bovo, Andrea, De Angelis, Tiziano, Issoglio, Elena
Rok vydání:	2022
Předmět:	Mathematics - Optimization and Control Mathematics - Analysis of PDEs Mathematics - Probability 91A05 91A15 60G40 93E20 49J40 35K58
Druh dokumentu:	Working Paper
Popis:	We study a class of zero-sum games between a singular-controller and a stopper over finite-time horizon. The underlying process is a multi-dimensional (locally non-degenerate) 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 obstacle constraint and 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. Comment: 38 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2203.06247 Zobrazit plný text záznamu View this record from Arxiv