Regularity of Nash payoffs of Markovian nonzero-sum stochastic differential games

被引：4

作者：

Hamadene, Said ^{[1
]}

Mannucci, Paola ^{[2
]}

机构：

[1] Le Mans Univ, LMM, Le Mans 9, France

[2] Univ Padua, Dipartimento Matemat Tullio Levi Civita, Padua, Italy

来源：

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES | 2019年 / 91卷 / 05期

关键词：

Nash equilibrium point; nonzero-sum stochastic differential game; nash payoff; backward SDE; HJBI system of equations; Sobolev space; EQUILIBRIUM POINTS;

D O I：

10.1080/17442508.2018.1540627

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we deal with the problem of existence of a smooth solution of the Hamilton-Jacobi-Bellman-Isaacs (HJBI for short) system of equations associated with nonzero-sum stochastic differential games. We consider the problem in unbounded domains either in the case of continuous generators or for discontinuous ones. In each case we show the existence of a smooth solution of the system. As a consequence, we show that the game has smooth Nash payoffs which are given by means of the solution of the HJBI system and the stochastic process which governs the dynamic of the controlled system.

引用

页码：695 / 715

页数：21