Title

A Variational Formula For Stochastic Controls And Some Applications

Keywords

Differential games; Maximum principle; Minimax principle; Nash equilibrium; Saddle point; Stochastic controls; Sufficient condition; Variational formula

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.

Publication Date

1-1-2007

Publication Title

Pure and Applied Mathematics Quarterly

Volume

3

Issue

2

Number of Pages

539-567

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.4310/PAMQ.2007.v3.n2.a7

Socpus ID

49649090400 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/49649090400

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