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COAR Access Rights: metadata only accessSubject: Stochastic optimal control

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    Article
    Citation - WoS: 3
    Citation - Scopus: 6
    A Discrete Optimality System for an Optimal Harvesting Problem
    (Springer Heidelberg, 2017) Bakan, Hacer Oz; Yilmaz, Fikriye; Weber, Gerhard-Wilhelm; Öz Bakan, Hacer
    In this paper, we obtain the discrete optimality system of an optimal harvesting problem. While maximizing a combination of the total expected utility of the consumption and of the terminal size of a population, as a dynamic constraint, we assume that the density of the population is modeled by a stochastic quasi-linear heat equation. Finite-difference and symplectic partitioned Runge-Kutta (SPRK) schemes are used for space and time discretizations, respectively. It is the first time that a SPRK scheme is employed for the optimal control of stochastic partial differential equations. Monte-Carlo simulation is applied to handle expectation appearing in the cost functional. We present our results together with a numerical example. The paper ends with a conclusion and an outlook to future studies, on further research questions and applications.
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    Article
    Citation - WoS: 5
    Citation - Scopus: 3
    An Approach for Regime-Switching Stochastic Control Problems With Memory and Terminal Conditions
    (Taylor & Francis Ltd, 2026) Savku, E.
    In this research article, we focus on a stochastic optimal control problem with two types of terminal constraints. These specific conditions provide real-valued and stochastic Lagrange multipliers. Our model evolves according to a Markov regime-switching jump diffusion model with memory. In this context, the memory is represented by a Stochastic Differential Delay Equation. We present two theorems for each constraint within the general formulation of stochastic optimal control theory in a Lagrangian environment. We approach to this task from a theoretical perspective and provide mild technical assumptions, which make our theorems applicable for a broad class of stochastic control problems as well as for a wide range of disciplines such as engineering, biology, operations research, medicine, computer science and economics. In this work, we apply Stochastic Maximum Principle to demonstrate an optimal dividend policy corresponding to a time-delayed wealth process of a company. Moreover, we determine the real-valued Lagrange multiplier of this control problem explicitly.