Open AccessOpen-loop equilibriums for a general class of time-inconsistent stochastic optimal control problems
Author(s) -
Ishak Alia
Publication year - 2023
Publication title -
mathematical control and related fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.658
H-Index - 21
eISSN - 2156-8472
pISSN - 2156-8499
DOI - 10.3934/mcrf.2021053
Subject(s) - mathematics , class (philosophy) , stochastic differential equation , jump diffusion , discounting , exponential function , dynamic inconsistency , portfolio , selection (genetic algorithm) , mathematical economics , jump , open loop controller , interval (graph theory) , optimal control , mathematical optimization , computer science , mathematical analysis , economics , closed loop , finance , physics , quantum mechanics , control engineering , artificial intelligence , combinatorics , engineering
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.