Researcher:
Tunç, Sait

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Master Student

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Sait

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Tunç

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Tunç, Sait

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2012 - 20153

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Researcher Of Publications: search.filters.isAuthorOfPublication.efd8421a-9af7-4208-8f28-3c854a1a6a2c

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Now showing 1 - 3 of 3
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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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    A deterministic analysis of an online convex mixture of experts algorithm
    (Institute of Electrical and Electronics Engineers (IEEE), 2015) Özkan, Hüseyin; Dönmez, Mehmet A.; N/A; Tunç, Sait; Master Student; Graduate School of Sciences and Engineering; N/A
    We analyze an online learning algorithm that adaptively combines outputs of two constituent algorithms (or the experts) running in parallel to estimate an unknown desired signal. This online learning algorithm is shown to achieve and in some cases outperform the mean-square error (MSE) performance of the best constituent algorithm in the steady state. However, the MSE analysis of this algorithm in the literature uses approximations and relies on statistical models on the underlying signals. Hence, such an analysis may not be useful or valid for signals generated by various real-life systems that show high degrees of nonstationarity, limit cycles and that are even chaotic in many cases. In this brief, we produce results in an individual sequence manner. In particular, we relate the time-accumulated squared estimation error of this online algorithm at any time over any interval to the one of the optimal convex mixture of the constituent algorithms directly tuned to the underlying signal in a deterministic sense without any statistical assumptions. In this sense, our analysis provides the transient, steady-state, and tracking behavior of this algorithm in a strong sense without any approximations in the derivations or statistical assumptions on the underlying signals such that our results are guaranteed to hold. We illustrate the introduced results through examples.
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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.