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April, 2023 A Minimum Principle for Stochastic Optimal Control Problem with Interval Cost Function
Mahdi Rezaei Bahrmand, Hamid Khaloozadeh, Parastoo Reihani Ardabili
Author Affiliations +
Taiwanese J. Math. 27(2): 401-416 (April, 2023). DOI: 10.11650/tjm/221102

Abstract

In this paper, we study an optimal control problem in which their cost function is interval-valued. Also, a stochastic differential equation governs their state space. Moreover, we introduce a generalized version of Bellman's optimality principle for the stochastic system with an interval-valued cost function. Also, we obtain the Hamilton–Jacobi–Bellman equations and their control decisions. Two numerical examples happen in finance in which their cost function are interval-valued functions, illustrating the efficiency of the discussed results. The obtained results provide significantly reliable decisions compared to the case where the conventional cost function is applied.

Citation

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Mahdi Rezaei Bahrmand. Hamid Khaloozadeh. Parastoo Reihani Ardabili. "A Minimum Principle for Stochastic Optimal Control Problem with Interval Cost Function." Taiwanese J. Math. 27 (2) 401 - 416, April, 2023. https://doi.org/10.11650/tjm/221102

Information

Received: 1 September 2022; Revised: 24 October 2022; Accepted: 4 November 2022; Published: April, 2023
First available in Project Euclid: 14 November 2022

MathSciNet: MR4563523
zbMATH: 1518.93152
Digital Object Identifier: 10.11650/tjm/221102

Subjects:
Primary: 65G30 , 91Gxx , 93E20

Keywords: dynamic programming , Hamilton–Jacobi–Bellman equation , interval cost function , Stochastic differential equation , stochastic optimal control , uncertainty

Rights: Copyright © 2023 The Mathematical Society of the Republic of China

Vol.27 • No. 2 • April, 2023
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