A Mean-Field Stochastic Maximum Principle for Optimal Control of Forward-Backward Stochastic Differential Equations with Jumps via Malliavin Calculus - Journal of Applied Mathematics and Physics

JAMP > Vol.6 No.1, January 2018

Journal of Applied Mathematics and Physics

Volume 6, Issue 1 (January 2018)

ISSN Print: 2327-4352 ISSN Online: 2327-4379

Google-based Impact Factor: 0.70 Citations

A Mean-Field Stochastic Maximum Principle for Optimal Control of Forward-Backward Stochastic Differential Equations with Jumps via Malliavin Calculus ()

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DOI: 10.4236/jamp.2018.61014 893 Downloads 1,959 Views Citations

Author(s)

Qing Zhou^1*, Yong Ren²

Affiliation(s)

¹School of Science, Beijing University of Posts and Telecommunications, Beijing, China.
²Department of Mathematics, Anhui Normal University, Wuhu, China.

ABSTRACT

This paper considers a mean-field type stochastic control problem where the dynamics is governed by a forward and backward stochastic differential equation (SDE) driven by Lévy processes and the information available to the controller is possibly less than the overall information. All the system coefficients and the objective performance functional are allowed to be random, possibly non-Markovian. Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed.

KEYWORDS

Malliavin Calculus, Maximum Principle, Forward-Backward Stochastic Differential Equations, Mean-Field Type, Jump Diffusion, Partial Information

Share and Cite:

Zhou, Q. and Ren, Y. (2018) A Mean-Field Stochastic Maximum Principle for Optimal Control of Forward-Backward Stochastic Differential Equations with Jumps via Malliavin Calculus. Journal of Applied Mathematics and Physics, 6, 138-154. doi: 10.4236/jamp.2018.61014.

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