Abstract
In this paper, we study the stochastic maximum principle for optimal control problem of anticipated forward-backward system with delay and Lévy processes as the random disturbance. This control system can be described by the anticipated forward-backward stochastic differential equations with delay and Lévy processes (AFBSDEDLs), we first obtain the existence and uniqueness theorem of adapted solutions for AFBSDEDLs; combining the AFBSDEDLs’ preliminary result with certain classical convex variational techniques, the corresponding maximum principle is proved.
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Supported by the National Natural Science Foundation (11221061 and 61174092), 111 project (B12023), the National Science Fund for Distinguished Young Scholars of China (11125102) and Youth Foundation of QiLu Normal Institute (2012L1010).
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Li, N., Wu, Z. Maximum principle for anticipated recursive stochastic optimal control problem with delay and Lévy processes. Appl. Math. J. Chin. Univ. 29, 67–85 (2014). https://doi.org/10.1007/s11766-014-3171-9
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DOI: https://doi.org/10.1007/s11766-014-3171-9