395 research outputs found
Partial Information Differential Games for Mean-Field SDEs
This paper is concerned with non-zero sum differential games of mean-field
stochastic differential equations with partial information and convex control
domain. First, applying the classical convex variations, we obtain stochastic
maximum principle for Nash equilibrium points. Subsequently, under additional
assumptions, verification theorem for Nash equilibrium points is also derived.
Finally, as an application, a linear quadratic example is discussed. The unique
Nash equilibrium point is represented in a feedback form of not only the
optimal filtering but also expected value of the system state, throughout the
solutions of the Riccati equations.Comment: 7 page
Stochastic Differential Games and Viscosity Solutions of Hamilton-Jacobi-Bellman-Isaacs Equations
In this paper we study zero-sum two-player stochastic differential games with
the help of theory of Backward Stochastic Differential Equations (BSDEs). At
the one hand we generalize the results of the pioneer work of Fleming and
Souganidis by considering cost functionals defined by controlled BSDEs and by
allowing the admissible control processes to depend on events occurring before
the beginning of the game (which implies that the cost functionals become
random variables), on the other hand the application of BSDE methods, in
particular that of the notion of stochastic "backward semigroups" introduced by
Peng allows to prove a dynamic programming principle for the upper and the
lower value functions of the game in a straight-forward way, without passing by
additional approximations. The upper and the lower value functions are proved
to be the unique viscosity solutions of the upper and the lower
Hamilton-Jacobi-Bellman-Isaacs equations, respectively. For this Peng's BSDE
method is translated from the framework of stochastic control theory into that
of stochastic differential games.Comment: The results were presented by Rainer Buckdahn at the "12th
International Symposium on Dynamic Games and Applications" in
Sophia-Antipolis (France) in June 2006; They were also reported by Juan Li at
2nd Workshop on "Stochastic Equations and Related Topics" in Jena (Germany)
in July 2006 and at one seminar in the ETH of Zurich in November 200
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