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Fully coupled mean‐field FBSDEs with jumps and related optimal control problems
Author(s) -
Li Wenqiang,
Min Hui
Publication year - 2020
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2677
Subject(s) - uniqueness , mathematics , stochastic differential equation , monotonic function , maximum principle , optimal control , mean field theory , stochastic control , property (philosophy) , mathematical optimization , variance (accounting) , mathematical analysis , physics , philosophy , accounting , epistemology , quantum mechanics , business
Summary In this article, we study a type of fully coupled mean‐field forward‐backward stochastic differential equations with jumps under the monotonicity condition, including the existence and the uniqueness of the solution of our equations as well as the continuity property of the solutions with respect to the parameters. Then we establish the stochastic maximum principle for the corresponding optimal control problems and give the applications to the mean‐variance portfolio problem and linear‐quadratic problem, respectively.