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Linear-quadratic mean-field type stackelberg differential games for stochastic jump-diffusion systems
doi: 10.3934/mcrf.2021053
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Open-loop equilibriums for a general class of time-inconsistent stochastic optimal control problems
Ishak Alia
Institute of Optics and Precision Mechanics, Ferhat Abbas University Setif 1, 19000 Setif, Algeria
Received February 2021 Revised August 2021 Early access October 2021
This paper studies open-loop equilibriums for a general class of time-inconsistent stochastic control problems under jump-diffusion SDEs with deterministic coefficients. Inspired by the idea of Four-Step-Scheme for forward-backward stochastic differential equations with jumps (FBSDEJs, for short), we derive two systems of integro-partial differential equations (IPDEs, for short). Then, we rigorously prove a verification theorem which provides a sufficient condition for open-loop equilibrium strategies. As special cases, a mean-variance portfolio selection problem and a time-inconsistent problem under non-exponential discounting are discussed.
Keywords: Time-inconsistency, stochastic control, open-loop equilibrium control, Poisson point process, parabolic integro-partial differential equations, mean-variance problem.
Mathematics Subject Classification: Primary: 91B51, 93E20, 60H30, 93E99, 60H10.
Citation: Ishak Alia. Open-loop equilibriums for a general class of time-inconsistent stochastic optimal control problems. Mathematical Control & Related Fields, doi: 10.3934/mcrf.2021053
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