Numerical Studies for Petrol and Gas Reservoir Problems

The focus of this project will be mathematical models to describe petroleum or gas reservoir simulations. For such a kind of problems, permeability is desperately needed in the oil industry, however, it is hard to accurately measure the permeability field in the earth, due to the large area of oil reservoir and complicated earth structure. Therefore, identification of permeability parameter is crucial for the efficiency of the mathematical models. Since the classical (deterministic) partial differential equations cannot express the behavior of the physical problem completely, the permeability parameter is represented as a random field.  The mathematical modelling of such a kind of problems corresponds to basically unsteady convection diffusion equations. Therefore, our first interest will be numerical investigation of the time-dependent convection diffusion equation with random input data. Then, we extend the concept to the stochastic optimal control problems. Lastly, by constructing the random data parameters as permeability with the help of the original data, the effect of the mathematical simulations can be observed.

Evaluation of Credit Risk Using Machine Learning Techniques in Banking Sector

In this project, credit scoring methods that are used in literature for credit risk assessment are taken into account. These methods do have great importance for lending institutions such as banks. Based on real life realizations, for credit scoring at first we aim to determine the significance of each variable in credit scoring. We test different combination of them to increase the performance of methods.

Improving Efficient and Secure SSL/TLS library

SSL/TLS protocols are used for the internet security. There are many cryptographic algorithms used in that protocol. This project is on improving an efficient and secure SSL/TLS library.

Secure and Efficient Block Cipher Design

Block ciphers are widely used for secure communication and data storage. This project aims to analyze the efficiency and security of the block ciphers. The side channel attacks and countermeasures are also studied.

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.