Title: Stochastic maximum principle for mean-field type singular optimal control problem with discounted cost

Authors: Muthukumar Palanisamy; Deepa Ravi

Addresses: Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram – 624 302, Tamilnadu, India ' Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram – 624 302, Tamilnadu, India

Abstract: In this article, mean-field type stochastic singular optimal control problem with discounted cost is studied over an infinite time interval. The discounted cost makes the cost functional is bounded, which guarantees the existence of optimal control. The control variable has two components as classical and singular control. Moreover the singular control satisfies bounded variation, non-decreasing continuous on the left with right limits. The proposed system is investigated in two different cases, such as without and with delay. In addition, infinite horizon version of stochastic maximum principle is established by using the convex control domain in each case. The obtained theoretical results are applied to optimal harvesting problem and optimal consumption problem.

Keywords: infinite horizon; mean-field; optimal control; singular control; stochastic maximum principle.

DOI: 10.1504/IJCSYSE.2019.101704

International Journal of Computational Systems Engineering, 2019 Vol.5 No.4, pp.235 - 242

Received: 27 Nov 2017
Accepted: 11 May 2018
Published online: 22 Aug 2019 *

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