Necessary First-Order and Second-Order Optimality Conditions in Discrete-Time Stochastic Systems

Mahmudov N.

Journal of Optimization Theory and Applications, vol.182, no.3, pp.1001-1018, 2019 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 182 Issue: 3
  • Publication Date: 2019
  • Doi Number: 10.1007/s10957-019-01478-y
  • Journal Name: Journal of Optimization Theory and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1001-1018
  • Keywords: Discrete-time backward stochastic equations, Discrete-time stochastic systems, Necessary conditions, Stochastic linear quadratic problem
  • Open Archive Collection: Article
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

In this paper, first-order and second-order necessary conditions for optimality for discrete-time stochastic optimal control problems governed by discrete-time Itô equations are established. A new discrete-time backward stochastic equation and discrete-time backward stochastic matrix equation are introduced. Based on the discrete-time backward stochastic Itô equation, a discrete-time stochastic maximum principle for the stochastic discrete optimal control problems is obtained. Moreover, using the discrete-time backward stochastic matrix equation the second-order necessary conditions for optimality are obtained.