Graduate School of Applied Mathematics
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Efficient implementation of TMVPbased prime field multiplication and its applications to ECC
(2019)The need for faster and practical cryptography is a research topic for decades. For elliptic curve cryptography, which is proposed independently by Koblitz and Miller in 1985 as a more efficient alternative to RSA, the ... 
Large sparse matrixvector multiplication over finite fields
(2019)Cryptographic computations such as factoring integers and computing discrete logarithms require solving a large sparse system of linear equations over finite fields. When dealing with such systems iterative solvers such ... 
Differential cryptanalysis on LBLOCK using differential factors
(2018)Cryptography had actually a long history and comes to today by evolving day by day. Now, it is a huge area in terms of the applications in industry and research topics in academia. Even if we do not realize, the cryptographic ... 
Efficient simulation and modelling of counterparty credit risk
(2018)After 20082009 crisis, measurement of Counterparty Credit risk has become an essential part of BaselIII regulations. The measurement involves a complex calculation, simulation and scenario generation process which involve ... 
Constructions of maximum rank distance codes, cyclic constant dimension codes, and subspace packings
(2018)In this thesis, we aim to introduce main contributions to solve three main problems in coding theory. The first problem investigates the construction of inequivalent maximum rank distance (MRD) codes. Namely, we look for ... 
Electricity load and price forecasting of Turkish electricity markets
(2018)Progress on the forecasting techniques of market clearing price (MCP) and system marginal price (SMP) conveys millions of dollars profit to the electricity generator corporations. Therefore, more accurate forecasting system ... 
Exit probabilities of constrained simple random walks
(2018)Consider a nearest neighbor stable two dimensional random walk X constrained to remain on the positive orthant. X is assumed stable, i.e., its average increment points toward the origin. X represents the lengths of two ... 
Exit probabilities of markov modulated constrained random walks
(2018)Let X be the constrained random walk on Z2+ with increments (0, 0), (1, 0), (−1, 1), (0, −1) whose jump probabilities are determined by the state of a finite state Markov chain M. X represents the lengths of two queues of ... 
Uncertainty quantification of parameters in local volatility model via frequentist, bayesian and stochastic galerkin methods
(2018)In this thesis, we investigate and implement advanced methods to quantify uncertain parameter(s) in Dupire local volatility equation. The advanced methods investigated are Bayesian and stochastic Galerkin methods. These ... 
Modeling interest rates moving in a band
(2018)It is not uncommon to observe interest rates or currencies to move in a band or being subject to an upper and/or lower bound set by national central banks. The Turkish Central Bank is using the interest rate corridor system ... 
Adaptive multivariate solution schemes for inverse electrocardiography problem
(2018)Electrocardiographic Imaging (ECGI) is an emerging medical imaging modality to visualizetheheart’selectricalactivity. Ithasapromisingpotentialfordiagnosingcardiac abnormalities and facilitate the planning and execution of ... 
Pricing spread and basket options under markovmodulated models
(2018)This thesis first aims to study the evaluation of spread and basket options under the classical Markovmodulated framework, for which a transition in the Markov process leads to a switch in the model parameters. In this ... 
Optimal control in fluid flow problems with POD applications to FEM solutions
(2018)This study investigates the numerical solutions of optimal control problems constrained by the partial differential equations (PDEs) of laminar fluid flows and heat transfer with the model order reduction (MOR). This is ... 
Empirical comparison of portfolio risk diversification algorithms
(2018)The enhanced correlations during global ﬁnancial crisis has revealed that simple asset allocation portfolios prove to be not welldiversiﬁed across different risk factors, which makes the risk based asset allocation ... 
A Comparison of constant and stochastic volatility in Merton’s portfolio optimization problem
(2018)Merton's Portfolio Problem is a dynamic portfolio choice problem, which assumes asset returns and covariances are constant. There is well documented evidence that, stock returns and volatilities are correlated. Therefore, ... 
Numerical studies of Kortewegde Vries equation with random input data
(2018)Differential equations are the primary tool to mathematically model physical phenomena in industry and natural science and to gain knowledge about its features. Deterministic differential equations does not sufficiently ... 
Reinsurance pricing using exposure curve of two dependent risks
(2018)It is known that experience rating and exposure rating are used for insurance and reinsurance pricing by many practitioners. One of the main tools of exposure rating which is commonly used is exposure curves. It evaluates ... 
Volatility indexes and an implementation of the Turkish BIST 30 index
(2018)In 1993, by representing of CBOE Vix, global financial markets met volatility indexes. In 2003, methodology of the CBOE Vix is updated and it took the form which used today. Day after day, volatility indexes have attracted ... 
Homomorphic encryption for data security in cloud computing
(2018)Recently, cloud computing has grown into a popular aspect of the IT industry. Cloud computing provides a range of hardware and software resources to its customers,which they can access through the internet. With the rapid ... 
Measuring longevity risk on second pillar pension system: Turkey case
(2018)Pension systems, that have had the brightest period almost all over the world after World War II, began to have some difﬁculties with accessing maturity times of these systems. Financial crisis and doubts about the ...