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Article Citation - WoS: 2Citation - Scopus: 2A Normal Distribution on Time Scales With Application(Univ Nis, Fac Sci Math, 2022) Aksoy, Umit; Cuchta, Tom; Georgiev, Svetlin; Okur, Yeliz YolcuWe introduce a new normal distribution on time scales. Based on this generalized normal distribution, a Brownian motion is introduced and its quadratic variation is derived.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: 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.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: 27Citation - Scopus: 29Meir-Keeler Type Contractions on Modular Metric Spaces(Univ Nis, Fac Sci Math, 2018) Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; Rakocevic, VladimirIn this paper we introduce contraction mappings of Meir-Keeler types on modular metric spaces and investigate the existence and uniqueness of their fixed points. We give an example which demonstrates our theoretical results.
