Title: Stochastic pointwise second-order maximum principle for optimal continuous-singular control using variational approach

Authors: Nour El Houda Abada; Mokhtar Hafayed

Addresses: Laboratory of Mathematical Analysis, Probability and Optimizations, University of Biskra, P.O. Box 145 Biskra 07000, Algeria ' Laboratory of Mathematical Analysis, Probability and Optimizations, University of Biskra, P.O. Box 145 Biskra 07000, Algeria

Abstract: In this paper, we establish the second-order necessary conditions for optimal continuous-singular stochastic control, where the system is governed by nonlinear controlled Itô stochastic differential equation. The control process has two components, the first being absolutely continuous and the second of bounded variation, non-decreasing continuous on the right with left limits. Pointwise second-order maximum principle in terms of the martingale with respect to the time variable is proved. The control domain is assumed to be convex. In this paper, the continuous control variable enters into both the drift and the diffusion terms of the control systems. Our result is proved by using variational techniques under some convexity conditions.

Keywords: optimal control; stochastic continuous-singular control; pointwise second-order necessary conditions; variational method.

DOI: 10.1504/IJMIC.2023.130111

International Journal of Modelling, Identification and Control, 2023 Vol.42 No.3, pp.226 - 240

Received: 27 Feb 2022
Received in revised form: 27 Apr 2022
Accepted: 01 May 2022
Published online: 05 Apr 2023 *

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