A variational formula for stochastic controls and some applications

    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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