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A maximum principle for partial information backward stochastic control problems with applications
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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
Maximum Principle for Forward-Backward Doubly Stochastic Control Systems and Applications
The maximum principle for optimal control problems of fully coupled
forward-backward doubly stochastic differential equations (FBDSDEs in short) in
the global form is obtained, under the assumptions that the diffusion
coefficients do not contain the control variable, but the control domain need
not to be convex. We apply our stochastic maximum principle (SMP in short) to
investigate the optimal control problems of a class of stochastic partial
differential equations (SPDEs in short). And as an example of the SMP, we solve
a kind of forward-backward doubly stochastic linear quadratic optimal control
problems as well. In the last section, we use the solution of FBDSDEs to get
the explicit form of the optimal control for linear quadratic stochastic
optimal control problem and open-loop Nash equilibrium point for nonzero sum
differential games problem
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