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

Nazim I. Mahmudov ()
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Nazim I. Mahmudov: Eastern Mediterranean University

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 3, No 8, 1018 pages

Abstract: 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.

Keywords: Discrete-time backward stochastic equations; Necessary conditions; Discrete-time stochastic systems; Stochastic linear quadratic problem; 49K45; 93C55; 93E20 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-019-01478-y

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