First- and Second-Order Maximum Principles for Discrete-Time Stochastic Optimal Control With Recursive Utilities

This article deals with the discrete-time stochastic optimal control problems with recursive utilities under weakened convexity assumption. A new stochastic maximum principle is established. Moreover, by constructing two new adjoint equations and two new variational equations for the backward stocha...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2024-01, Vol.69 (1), p.43-54
Main Authors: Song, Teng, Liu, Bin
Format: Article
Language:English
Subjects:
Adjoint equations
Convexity
Difference equations
discrete-time stochastic systems
Discrete-time systems
Mathematical analysis
Mathematical models
Maximum principle
Optimal control
Optimization
Process control
recursive optimal control
stochastic maximum principle
Stochastic processes
Symmetric matrices
Utilities
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Summary:This article deals with the discrete-time stochastic optimal control problems with recursive utilities under weakened convexity assumption. A new stochastic maximum principle is established. Moreover, by constructing two new adjoint equations and two new variational equations for the backward stochastic difference equation, we obtain the second-order necessary optimality condition of quasi-singular control. Finally, as an illustration, a discrete-time mean-variance portfolio selection mixed with a recursive utility functional optimization problem is solved.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2023.3261345