Title

A variational formula for stochastic controls and some applications

Authors

Authors

L. B. Mou;J. M. Yong

Comments

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Abbreviated Journal Title

Pure Appl. Math. Q.

Keywords

stochastic controls; variational formula; maximum principle; differential games; minimax principle; sufficient condition; saddle; point; Nash equilibrium; MAXIMUM PRINCIPLE; DIFFERENTIAL-EQUATIONS; Mathematics, Applied; Mathematics

Abstract

For a controlled stochastic differential equation with a Bolza type performance functional, a variational formula for the functional in a given control process direction is derived, by means of backward stochastic differential equations. As applications, some Pontryagin type maximum principles are established for optimal controls of control problems, for saddle points of open-loop two-person zero-sum differential games, and for Nash equilibria of N-person nonzero-sum differential games. The results presented in this paper generalizes/simplifies the relevant ones found in [12] [17]. In addition, a sufficient existence condition of Nash equilibria is proved for nonzero-sum games.

Journal Title

Pure and Applied Mathematics Quarterly

Volume

3

Issue/Number

2

Publication Date

1-1-2007

Document Type

Article

Language

English

First Page

539

Last Page

567

WOS Identifier

WOS:000248974400008

ISSN

1558-8599

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