Bakan, Hacer Öz

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Hacer Öz, Bakan
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Bakan, Hacer Oz
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Hacer Oz, Bakan
Öz Bakan,H.
Job Title
Araştırma Görevlisi
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hacer.oz@atilim.edu.tr
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Scholarly Output

3

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2

Citation Count

13

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2017 - 20183
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    Citation Count: 0
    Itô–Taylor expansions for systems of stochastic differential equations with applications to stochastic partial differential equations
    (Springer New York LLC, 2017) Bakan, Hacer Öz; Öz Bakan,H.; Weber,G.-W.; Mathematics
    Stochastic differential equations (SDEs) are playing a growing role in financial mathematics, actuarial sciences, physics, biology and engineering. For example, in financial mathematics, fluctuating stock prices and option prices can be modeled by SDEs. In this chapter, we focus on a numerical simulation of systems of SDEs based on the stochastic Taylor series expansions. At first, we apply the vector-valued Itô formula to the systems of SDEs, then, the stochastic Taylor formula is used to get the numerical schemes. In the case of higher dimensional stochastic processes and equations, the numerical schemes may be expensive and take more time to compute. We deal with systems with standard n-dimensional systems of SDEs having correlated Brownian motions. One the main issue is to transform the systems of SDEs with correlated Brownian motions to the ones having standard Brownian motion, and then, to apply the Itô formula to the transformed systems. As an application, we consider stochastic partial differential equations (SPDEs). We first use finite difference method to approximate the space variable. Then, by using the stochastic Taylor series expansions we obtain the discrete problem. Numerical examples are presented to show the efficiency of the approach. The chapter ends with a conclusion and an outlook to future studies. © 2017, Springer International Publishing AG.
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    Article
    Citation Count: 9
    Minimal truncation error constants for Runge-Kutta method for stochastic optimal control problems
    (Elsevier, 2018) Bakan, Hacer Öz; Yilmaz, Fikriye; Weber, Gerhard-Wilhelm; 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.
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    Article
    Citation Count: 4
    A discrete optimality system for an optimal harvesting problem
    (Springer Heidelberg, 2017) Bakan, Hacer Öz; Yilmaz, Fikriye; Weber, Gerhard-Wilhelm; Mathematics
    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.