Volume 28, 2022
|Number of page(s)
|02 August 2022
A mean-field stochastic linear-quadratic optimal control problem with jumps under partial information*
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, PR China
2 Department of Mathematical Sciences, Huzhou University, Zhejiang 313000, PR China
** Corresponding author: firstname.lastname@example.org
Accepted: 1 May 2022
In this article, the stochastic linear-quadratic optimal control problem of mean-field type with jumps under partial information is discussed. The state equation which contains affine terms is a SDE with jumps driven by a multidimensional Brownian motion and a Poisson stochastic martingale measure, and the quadratic cost function contains cross terms. In addition, the state and the control as well as their expectations are contained both in the state equation and the cost functional. This is the so-called optimal control problem of mean-field type. Firstly, the existence and uniqueness of the optimal control is proved. Secondly, the adjoint processes of the state equation is introduced, and by using the duality technique, the optimal control is characterized by the stochastic Hamiltonian system. Thirdly, by applying a decoupling technology, we deduce two integro-differential Riccati equations and get the feedback representation of the optimal control under partial information. Fourthly, the existence and uniqueness of the solutions of two Riccati equations are proved. Finally, we discuss a special case, and establish the corresponding feedback representation of the optimal control by means of filtering technique.
Mathematics Subject Classification: 93E20 / 60H10
Key words: Mean-field / linear-quadratic optimal control / partial information / Hamiltonian system / feedback representation / adjoint processes / Riccati equation
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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