Volume 26, 2020
|Number of page(s)||39|
|Published online||13 November 2020|
A global maximum principle for optimal control of general mean-field forward-backward stochastic systems with jumps*
School of Statistics, Shandong University of Finance and Economics,
250014, P.R. China.
2 Department of Mathematics, Huzhou University, Zhejiang 313000, P.R. China.
** Corresponding author: email@example.com
Accepted: 10 February 2020
In this paper we prove a maximum principle of optimal control problem for a class of general mean-field forward-backward stochastic systems with jumps in the case where the diffusion coefficients depend on control, the control set does not need to be convex, the coefficients of jump terms are independent of control as well as the coefficients of mean-field backward stochastic differential equations depend on the joint law of (X(t), Y (t)). Since the coefficients depend on measure, higher mean-field terms could be involved. In order to analyse them, two new adjoint equations are brought in and several new generic estimates of their solutions are investigated. Utilizing these subtle estimates, the second-order expansion of the cost functional, which is the key point to analyse the necessary condition, is obtained, and where after the stochastic maximum principle. An illustrative application to mean-field game is considered.
Mathematics Subject Classification: 93E20 / 60H10
Key words: Stochastic control / global maximum principle / general mean-field forward-backward stochastic differential equation with jumps
T. Hao work has been supported by National Natural Science Foundation of China (Grant Nos. 71671104, 11871309, 11801315, 11801317, 71803097), the Ministry of Education of Humanities and Social Science Project (Grant No. 16YJA910003), Natural Science Foundation of Shandong Province (No. ZR2018QA001, ZR2019MA013), A Project of Shandong Province Higher Educational Science and Technology Program (Grant Nos. J17KA162, J17KA163), and Incubation Group Project of Financial Statistics and Risk Management of SDUFE. Q.X. Meng work has been supported by the National Natural Science Foundation of China (Grant No. 11871121) and the Natural Science Foundation of Zhejiang Province for Distinguished Young Scholar (Grant No. LR15A010001).
© EDP Sciences, SMAI 2020
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