Two-person zero-sum linear quadratic stochastic differential games by a Hilbert space method

    Authors

    L. B. Mou;J. M. Yong

    Comments

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    Abbreviated Journal Title

    J. Ind. Manag. Optim.

    Keywords

    stochastic games; open-loop controls; saddle points; linear-quadratic; Hilbert method; RICCATI EQUATION; Engineering, Multidisciplinary; Operations Research & Management; Science; Mathematics, Interdisciplinary Applications

    Abstract

    An open-loop two-person zero-sum linear quadratic (LQ for short) stochastic differential game is considered. The controls for both players are allowed to appear in both the drift and diffusion of the state equation, the weighting matrices in the payoff/cost functional are not assumed to be definite/non-singular, and the cross-terms between two controls are allowed to appear. A forward-backward stochastic differential equation (FBSDE, for short) and a generalized differential Riccati equation are introduced, whose solvability leads to the existence of the open-loop saddle points for the corresponding two-person zero-sum LQ stochastic differential game, under some additional mild conditions. The main idea is a thorough study of general two-person zero-sum LQ games in Hilbert spaces.

    Journal Title

    Journal of Industrial and Management Optimization

    Volume

    2

    Issue/Number

    1

    Publication Date

    1-1-2006

    Document Type

    Article

    Language

    English

    First Page

    95

    Last Page

    117

    WOS Identifier

    WOS:000240983100007

    ISSN

    1547-5816

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