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Article Citation - WoS: 2Citation - Scopus: 2Optimal Limit Order Book Trading Strategies With Stochastic Volatility in the Underlying Asset(Springer, 2023) Aydogan, Burcu; Ugur, Omur; Aksoy, UmitIn quantitative finance, there have been numerous new aspects and developments related with the stochastic control and optimization problems which handle the controlled variables of performing the behavior of a dynamical system to achieve certain objectives. In this paper, we address the optimal trading strategies via price impact models using Heston stochastic volatility framework including jump processes either in price or in volatility of the price dynamics with the aim of maximizing expected return of the trader by controlling the inventories. Two types of utility functions are considered: quadratic and exponential. In both cases, the remaining inventories of the market maker are charged with a liquidation cost. In order to achieve the optimal quotes, we control the inventory risk and follow the influence of each parameter in the model to the best bid and ask prices. We show that the risk metrics including profit and loss distribution (PnL), standard deviation and Sharpe ratio play important roles for the trader to make decisions on the strategies. We apply finite differences and linear interpolation as well as extrapolation techniques to obtain a solution of the nonlinear Hamilton-Jacobi-Bellman (HJB) equation. Moreover, we consider different cases on the modeling to carry out the numerical simulations.Article Citation - WoS: 51Citation - Scopus: 58F-Contraction Mappings on Metric-Like Spaces in Connection With Integral Equations on Time Scales(Springer-verlag Italia Srl, 2020) Agarwal, Ravi P.; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.In this paper we investigate the existence and uniqueness of fixed points of certain (phi,F)-type contractions in the frame of metric-like spaces. As an application of the theorem we consider the existence and uniqueness of solutions of nonlinear Fredholm integral equations of the second kind on time scales. We also present a particular example which demonstrates our theoretical results.Article Polynomial Logistic Distribution Associated With a Cubic Polynomial(Taylor & Francis inc, 2017) Aksoy, Umit; Ostrovska, Sofiya; Ozban, Ahmet YasarLet P(x) be a polynomial monotone increasing on ( - , +). The probability distribution possessing the distribution function is called the polynomial logistic distribution with associated polynomial P. This has recently been introduced by Koutras etal., who have also demonstrated its importance for modeling financial data. In this article, the properties of the polynomial logistic distribution with an associated polynomial of degree 3 have been investigated in detail. An example of polynomial logistic distribution describing daily exchange rate fluctuations for the US dollar versus the Turkish lira is provided.Article Citation - WoS: 16Citation - Scopus: 18Weak Ψ-Contractions on Partially Ordered Metric Spaces and Applications To Boundary Value Problems(Springeropen, 2014) Karapinar, Erdal; Erhan, Inci M.; Aksoy, UmitA class of weak psi-contractions satisfying the C-condition is defined on metric spaces. The existence and uniqueness of fixed points of such maps are discussed both on metric spaces and on partially ordered metric spaces. The results are applied to a first order periodic boundary value problem.Article Citation - WoS: 11Citation - Scopus: 14Schwarz Problem for Higher-Order Complex Partial Differential Equations in the Upper Half Plane(Wiley-v C H verlag Gmbh, 2019) Aksoy, Umit; Begehr, Heinrich; Celebi, A. OkayLinear and nonlinear elliptic complex partial differential equations of higher-order are considered under Schwarz conditions in the upper-half plane, Firstly, using the integral representations for the solutions of the inhomogeneous polyanalytic equation with Schvvarz conditions, a class of integral operators is introduced together with some of their properties. Then, these operators are used to transform the problem for linear equations into singular integral equations. In the case of nonlinear equations such a transformation yields a system of integro-differential equations. Existence of the solutions of the relevant boundary value problems for linear and nonlinear equations are discussed via Fredholm theory and fixed point theorems, respectively.Article Citation - WoS: 3Citation - Scopus: 3On the Fixed Points of Iterative Contractive Mappings Defined Via Implicit Relation(Taylor & Francis Ltd, 2021) Aksoy, Umit; Erhan, Inci M.; Fulga, Andreea; Karapinar, ErdalIn this paper, we consider an implicit relation to generalize iterative fixed point results in the literature in the context of metric spaces. We conclude that several existing results are immediate consequences of our main results.Article Citation - WoS: 141Citation - Scopus: 144Uniqueness of Solution for Higher-Order Nonlinear Fractional Differential Equations With Multi-Point and Integral Boundary Conditions(Springer-verlag Italia Srl, 2021) Sevinik-Adiguzel, Rezan; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.This study is devoted to the development of alternative conditions for existence and uniqueness of nonlinear fractional differential equations of higher-order with integral and multi-point boundary conditions. It uses a novel approach of employing a fixed point theorem based on contractive iterates of the integral operator for the corresponding fixed point problem. We start with developing an existence-uniqueness theorem for self-mappings with contractive iterate in a b-metric-like space. Then, we obtain the unique solvability of the problem under suitable conditions by utilizing an appropriate b-metric-like space.Article Dirichlet-Type Problems for n-poisson Equation in Clifford Analysis(Taylor & Francis Ltd, 2022) Aksoy, Umit; Celebi, A. OkayIterated Dirichlet problem, also called as Riquier or Navier problem, and polyharmonic Dirichlet problem are studied for n-Poisson equation in Clifford analysis using iterated polyharmonic Green function and polyharmonic Green-Almansi type function appropriate for the boundary conditions of the problems.Article Citation - WoS: 1Citation - Scopus: 1Several Outcomes of Fixed-Point Theory in Interpolative Metric Spaces(Univ Politecnica Valencia, Editorial UPV, 2025) Karapinar, Erdal; Kadioglu, Kaan; Turkmenel, Merve Gulcin; Aksoy, UmitThis paper aims to generalize and improve the recent fixed-point theorems in the setting of interpolative metric spaces. More precisely, we investigate the existence and uniqueness of the fixed-point for certain operators of the Ciric-Reich-Rus-type, via admissible mapping in the context of interpolative metric spaces.
