Browsing by Author "Bakan, Hacer Oz"

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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
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.
Citation - WoS: 10
Citation - Scopus: 11
Minimal Truncation Error Constants for Runge-Kutta Method for Stochastic Optimal Control Problems
(Elsevier, 2018) Bakan, Hacer Oz; Bakan, Hacer Öz; Yilmaz, Fikriye; Weber, Gerhard-Wilhelm; Bakan, Hacer Öz; Mathematics; Mathematics
In this work, we obtain strong order-1 conditions with minimal truncation error constants of Runge-Kutta method for the optimal control of stochastic differential equations (SDEs). We match Stratonovich-Taylor expansion of the exact solution with Stratonovich-Taylor expansion of our approximation method that is defined by the Runge-Kutta scheme, term by term, in order to get the strong order-1 conditions. By a conclusion and an outlook to future research, the paper ends. (C) 2017 Elsevier B.V. All rights reserved.