INSTITUTE OF APPLIED MATHEMATICS
A Real-Time Working Prototype for Algorithmic Trading and Financial Tools

In this work, it is planned to create a real time algorithmic trading prototype. This prototype is designed as a system that generates data in itself and uses this data, and also can use real market data when necessary. Models in this system will generate artificial market data and portfolio analysis and optimization techniques will be examined using algorithmic trading techniques. In this system, various areas of finance engineering such as pricing, simulation, risk analysis and optimization wil be used. The prototype is designed as a flexible system in that modules can be developed and new modules can be added.

Modeling the Factors in Capital Requirement Criteria for Life and Non-life Insurance Companies

Aim of this project is to determine the factors which are effective under the framework of Solvency II for both life and non-life insurances and to propose a comprehensive model which is based on these factors. In addition, the validity of the dependence measurements suggested by existing standard model and under the framework of regulations for Turkish sector will be discussed via copula approach.

Protection in Statistical Data Bases under Differential Privacy

The aim of this project is to create a masking methodology on financial data sets while ensuring the confidentiality of the data. The techniques to obtain sanitized data and test the accuracy for selected statistical analyses on masked data are determined. The possible attacks deciphering the proposed methodologies are studied and the ways to prevent them are targeted to be implemented into the privacy module. A user-friendly software, to generate a secure masked data set from the original data for the purposes of quantifying certain statistical methods is aimed to be prepared.

Backward Stochastic Differential Equations with Singular Terminal Values and Applications in Finance

This project  focuses on this type of BSDE where the terminal condition is allowed to depend on the entire path of the underlying process; we call such terminal conditions ''Non-Markovian.'' The goal is to construct solutions for a range of non-Markovian singular terminal values under various assumptions, and to understand, to the best of our ability, to what extent such BSDE can be solved. We will also explore possible applications of our results to finance. In a financial context, non-Markovian terminal conditions correspond to specifying conditions under which the liquidation takes place.

Numerical Studies of Korteweg-de Vries Equation with Random Input Data

Differential equations are  primary tools to mathematically model physical phenomena in industry and natural science and to gain knowledge about its features. However, classical deterministic differential equations does not sufficiently model physically observed phenomena since there exit naturally inevitable uncertainties in nature. The aim of this project is to investigate numerical solutions of Korteweg-de Vries (KdV) equation with  random input data, which is a fundamental differential equation for modeling and describing solitary waves occurring in nature.