Researcher:
Dönmez, Mehmet Ali

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Master Student

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Mehmet Ali

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Dönmez

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Dönmez, Mehmet Ali

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2012 - 201313

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Researcher Of Publications: search.filters.isAuthorOfPublication.c9a99f1c-2118-41fc-9932-b5b062bb7467

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Now showing 1 - 10 of 13
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    Growth optimal investment with threshold rebalancing portfolios under transaction costs
    (Institute of Electrical and Electronics Engineers (IEEE), 2013) Tunc, Sait; Kozat, Suleyman S.; N/A; Dönmez, Mehmet Ali; Master Student; Graduate School of Sciences and Engineering; N/A
    We study how to invest optimally in a stock market having a finite number of assets from a signal processing perspective. In particular, we introduce a portfolio selection algorithm that maximizes the expected cumulative wealth in i.i.d. two-asset discrete-time markets where the market levies proportional transaction costs in buying and selling stocks. This is achieved by using 'threshold rebalanced portfolios', where trading occurs only if the portfolio breaches certain thresholds. Under the assumption that the relative price sequences have log-normal distribution from the Black-Scholes model, we evaluate the expected wealth under proportional transaction costs and find the threshold rebalanced portfolio that achieves the maximal expected cumulative wealth over any investment period.
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    Transient analysis of convexly constrained mixture methods
    (IEEE, 2012) N/A; Department of Electrical and Electronics Engineering; N/A; N/A; Kozat, Süleyman Serdar; Dönmez, Mehmet Ali; Özkan, Hüseyin; Faculty Member; Master Student; PhD Student; Department of Electrical and Electronics Engineering; College of Engineering; Graduate School of Sciences and Engineering; Graduate School of Sciences and Engineering; 177972; N/A; N/A
    We study the transient performances of three convexly constrained adaptive combination methods that combine outputs of two adaptive filters running in parallel to model a desired unknown system. We propose a theoretical model for the mean and mean-square convergence behaviors of each algorithm. Specifically, we provide expressions for the time evolution of the mean and the variance of the combination parameters, as well as for the mean square errors. The accuracy of the theoretical models are illustrated through simulations in the case of a mixture of two LMS filters with different step sizes.
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    Optimal portfolios under transaction costs in discrete time markets
    (IEEE, 2012) N/A; Department of Electrical and Electronics Engineering; N/A; N/A; Kozat, Süleyman Serdar; Dönmez, Mehmet Ali; Tunç, Sait; Faculty Member; Master Student; Master Student; Department of Electrical and Electronics Engineering; College of Engineering; Graduate School of Sciences and Engineering; Graduate School of Sciences and Engineering; 177972; N/A; N/A
    We study portfolio investment problem from a probabilistic modeling perspective and study how an investor should distribute wealth over two assets in order to maximize the cumulative wealth. We construct portfolios that provide the optimal growth in i.i.d. discrete time two-asset markets under proportional transaction costs. As the market model, we consider arbitrary discrete distributions on the price relative vectors. To achieve optimal growth, we use threshold portfolios. We demonstrate that under the threshold rebalancing framework, the achievable set of portfolios elegantly form an irreducible Markov chain under mild technical conditions. We evaluate the corresponding stationary distribution of this Markov chain, which provides a natural and efficient method to calculate the cumulative expected wealth. Subsequently, the corresponding parameters are optimized using a brute force approach yielding the growth optimal portfolio under proportional transaction costs in i.i.d. discrete-time two-asset markets.
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    Optimal investment under transaction costs: a threshold rebalanced portfolio approach
    (IEEE-Inst Electrical Electronics Engineers Inc, 2013) Tunç, Sait; Kozat, Süleyman Serdar; N/A; Dönmez, Mehmet Ali; Master Student; Graduate School of Sciences and Engineering; N/A
    We study how to invest optimally in a financial market having a finite number of assets from a signal processing perspective. Specifically, we investigate how an investor should distribute capital over these assets and when he/she should reallocate the distribution of the funds over these assets to maximize the expected cumulative wealth over any investment period. In particular, we introduce a portfolio selection algorithm that maximizes the expected cumulative wealth in i.i.d. two-asset discrete-time markets where the market levies proportional transaction costs in buying and selling stocks. We achieve this using "threshold rebalanced portfolios", where trading occurs only if the portfolio breaches certain thresholds. Under the assumption that the relative price sequences have log-normal distribution from the Black-Scholes model, we evaluate the expected wealth under proportional transaction costs and find the threshold rebalanced portfolio that achieves the maximal expected cumulative wealth over any investment period. Our derivations can be readily extended to markets having more than two stocks, where these extensions are provided in the paper. As predicted from our derivations, we significantly improve the achieved wealth with respect to the portfolio selection algorithms from the literature on historical data sets under both mild and heavy transaction costs.
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    Steady state MSE analysis of convexly constrained mixture methods
    (IEEE, 2012) N/A; Department of Electrical and Electronics Engineering; N/A; Kozat, Süleyman Serdar; Dönmez, Mehmet Ali; Faculty Member; Master Student; Department of Electrical and Electronics Engineering; College of Engineering; Graduate School of Sciences and Engineering; 177972; N/A
    We study the steady-state performances of four convexly constrained mixture algorithms that adaptively combine outputs of two adaptive filters running in parallel to model an unknown system. We demonstrate that these algorithms are universal such that they achieve the performance of the best constituent filter in the steady-state if certain algorithmic parameters are chosen properly. We also demonstrate that certain mixtures converge to the optimal convex combination filter such that their steady-state performances can be better than the best constituent filter. Furthermore, we show that the investigated convexly constrained algorithms update certain auxiliary variables through sigmoid nonlinearity, hence, in this sense, related.
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    Growth optimal portfolios in discrete-time markets under transaction costs
    (IEEE-Inst Electrical Electronics Engineers Inc, 2012) N/A; Department of Electrical and Electronics Engineering; N/A; N/A; Kozat, Süleyman Serdar; Dönmez, Mehmet Ali; Tunç, Sait; Faculty Member; Master Student; Master Student; Department of Electrical and Electronics Engineering; College of Engineering; Graduate School of Sciences and Engineering; Graduate School of Sciences and Engineering; 177972; N/A; N/A
    We investigate portfolio selection problem from a signal processing perspective and study how and when an investor should diversify wealth over two assets in order to maximize the cumulative wealth. We construct portfolios that provide the optimal growth in i.i.d. discrete time two-asset markets under proportional transaction costs. As the market model, we consider arbitrary discrete distributions on the price relative vectors, which can also be used to approximate a wide class of continuous distributions. To achieve optimal growth, we use threshold portfolios, where we introduce an iterative algorithm to calculate the expected wealth. Subsequently, the corresponding parameters are optimized using a brute force approach yielding the growth optimal portfolio under proportional transaction costs in i.i.d. discrete-time two-asset markets.
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    Competitive least squares problem with bounded data uncertainties
    (IEEE, 2012) N/A; Department of Electrical and Electronics Engineering; N/A; N/A; Kozat, Süleyman Serdar; Dönmez, Mehmet Ali; Kalantarova, Nargiz; Faculty Member; Master Student; PhD Student; Department of Electrical and Electronics Engineering; College of Engineering; Graduate School of Sciences and Engineering; Graduate School of Sciences and Engineering; 177972; N/A; N/A
    We study robust least squares problem with bounded data uncertainties in a competitive algorithm framework. We propose a competitive least squares (LS) approach that minimizes the worst case “regret” which is the difference between the squared data error and the smallest attainable squared data error of an LS estimator. We illustrate that the robust least squares problem can be put in an SDP form for both structured and unstructured data matrices and uncertainties. Through numerical examples we demonstrate the potential merit of the proposed approaches.
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    Adaptive mixture methods based on Bregman divergences
    (IEEE, 2012) N/A; Department of Electrical and Electronics Engineering; N/A; N/A; Kozat, Süleyman Serdar; Dönmez, Mehmet Ali; İnan, Hüseyin Atahan; Faculty Member; Master Student; PhD Student; Department of Electrical and Electronics Engineering; College of Engineering; Graduate School of Sciences and Engineering; Graduate School of Sciences and Engineering; 177972; N/A; N/A
    We investigate affinely constrained mixture methods adaptively combining outputs of m constituent filters running in parallel to model a desired signal. We use Bregman divergences and obtain multiplicative updates to train these linear combination weights under the affine constraints. We use the unnormalized relative entropy and the relative entropy that produce the exponentiated gradient update with unnormalized weights (EGU) and the exponentiated gradient update with positive and negative weights (EG), respectively. We carry out the mean and the mean-square transient analysis of the affinely constrained mixtures of m filters using the EGU or EG algorithms. We compare performances of different algorithms through our simulations and illustrate the accuracy of our results.
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    A novel adaptive diversity achieving channel estimation scheme for LTE
    (ACM, 2012) N/A; Department of Electrical and Electronics Engineering; N/A; Kozat, Süleyman Serdar; Dönmez, Mehmet Ali; Faculty Member; Master Student; Department of Electrical and Electronics Engineering; College of Engineering; Graduate School of Sciences and Engineering; 177972; N/A
    As the LTE standard becomes more widespread for wireless communication of high-speed data for mobile phones, the importance of channel estimation algorithms for OFDM is increasing. Although OFDM is widely used as the signal bearer in many different applications including LTE due to its robustness to multipath fading and interference, its success heavily depends on accurate channel estimation, especially, in rapidly changing urban environments. In this paper, we introduce an adaptive diversity achieving combination scheme operating at the receiver that is mathematically proven to improve channel estimation performance. Here, we introduce an adaptive combination of adaptive channel estimation algorithms running in parallel considered as diversity branches. The channel estimates of these constituent branches are combined using a convexly constrained adaptive mixture. Unlike the well-known diversity achieving schemes, including selection combining, threshold combining, this algorithm is mathematically shown to improve estimation or receiver operating performance. To this end, we first derive a multiplicative update rule based on Bregman divergences to train the combination weights. We then present the steady-state MSE analysis of the combination algorithm and show that the mixture is universal with respect to the input channel estimators such that it performs as well as the best constituent estimator, and in some cases, outperforms both constituent channel estimators in the steady-state. We also show that the mixture diversity weight vector converges to the optimal combination weight vector in terms of minimizing MSE under the convex constraint. We analyze and validate our analysis and the introduced results through simulations.
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    Steady state and transient mse analysis of convexly constrained mixture methods
    (IEEE-Inst Electrical Electronics Engineers Inc, 2012) N/A; Department of Electrical and Electronics Engineering; Dönmez, Mehmet Ali; Kozat, Süleyman Serdar; Master Student; Faculty Member; Department of Electrical and Electronics Engineering; Graduate School of Sciences and Engineering; College of Engineering; N/A; 177972
    We investigate convexly constrained mixture methods to adaptively combine outputs of two adaptive filters running in parallel to model a desired unknown system. We compare several algorithms with respect to their mean-square error in the steady state, when the underlying unknown system is nonstationary with a random walk model. We demonstrate that these algorithms are universal such that they achieve the performance of the best constituent filter in the steady state if certain algorithmic parameters are chosen properly. We also demonstrate that certain mixtures converge to the optimal convex combination filter such that their steady-state performances can be better than the best constituent filter. We also perform the transient analysis of these updates in the mean and mean-square error sense. Furthermore, we show that the investigated convexly constrained algorithms update certain auxiliary variables through sigmoid nonlinearity, hence, in this sense, related.