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Free, publicly-accessible full text available April 30, 2026
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Mei, Hongwei; Wei, Qingmeng; Yong, Jiongmin (, Numerical Algebra, Control and Optimization)
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Mei, Hongwei; Wei, Qingmeng; Yong, Jiongmin (, SIAM Journal on Control and Optimization)null (Ed.)
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Mei, Hongwei; Yong, Jiongmin (, ESAIM: Control, Optimisation and Calculus of Variations)An optimal control problem is considered for a stochastic differential equation containing a state-dependent regime switching, with a recursive cost functional. Due to the non-exponential discounting in the cost functional, the problem is time-inconsistent in general. Therefore, instead of finding a global optimal control (which is not possible), we look for a time-consistent (approximately) locally optimal equilibrium strategy. Such a strategy can be represented through the solution to a system of partial differential equations, called an equilibrium Hamilton–Jacob–Bellman (HJB) equation which is constructed via a sequence of multi-person differential games. A verification theorem is proved and, under proper conditions, the well-posedness of the equilibrium HJB equation is established as well.more » « less
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