Recently financial applications attracted a significant interest from the signal processing community since the global crises demonstrated the importance of sound financial modeling and reliable data processing. Financial markets produce vast amount of temporal data ranging from stock prices to interest rates making them ideal mediums to apply signal processing methods. Furthermore, due to the integration of high performance, low-latency computing recourses and financial data collection infrastructures, a wide range of signal processing algorithms could be readily leveraged with full potential in financial stock markets.

This project specifically focuses on the portfolio selection problem, which is one the most important financial applications and has already attracted substantial interest from the signal processing community. In particular, we study investment in a financial market having a finite number of assets. We concentrate on how an investor should distribute capital over these assets and when he/she should reallocate the distribution of the funds over those assets in time to maximize the overall cumulative wealth. In financial terms, distributing ones capital over various assets is known as the portfolio management problem and reallocation of this distribution by buying and selling stocks is referred as the rebalancing of the given portfolio. Due to obvious reasons, the portfolio management problem has been investigated in various different fields from financial engineering, machine learning to information theory, with a significant room for improvement as the recent financial crises demonstrated. To this end, we investigate the portfolio management problem in discrete-time markets when the market levies proportional transaction costs in trading while buying and selling stocks, which accurately models a wide range of real life markets.

Sample publications on this topic include:

-- S. Tunc, M. A. Donmez and S. S. Kozat, ``Growth Optimal Portfolios in Discrete-time Markets Under Transactions Costs,'' IEEE Transactions on Signal Processing, 2013.

-- N. D. Vanli, S. Tunc and S. S. Kozat, ``Robust Portfolio Selection in Discrete-time Markets Under Transaction Costs,'' Digital Signal Processing, 2013.

-- S. Tunc, S. S. Kozat, ``Optimal Investment Under Transaction Costs: A Threshold Rebalanced Portfolio Approach,'' IEEE Transactions on Signal Processing, vol. 61, issue 12, pp. 3129-3142, June 2013.

-- M. A. Donmez, S. Tunc, S. S. Kozat, ``Optimal Portfolios Under Transaction Costs in Discrete Time Markets," Proceedings of IEEE Workshop on Machine Learning for Signal Processing Workshop, 2012.

-- M. A. Donmez, S. Tunc, S. S. Kozat, ``Growth Optimal Portfolios in Discrete Time Markets Under Transaction Costs," Proceedings of IEEE Conference on Signal Processing Advances in Wireless Communications, 2012.

-- S. S. Kozat, A. C. Singer, ``Switching Strategies for Sequential Decision Problems with Multiplicative Loss with Application to Portfolios," IEEE Transactions on Signal Processing, vol. 57, issue 6, pp. 2192-2208, 2009.

-- S. S. Kozat, A. C. Singer, A. J. Bean, ``A Tree-Weighting Approach to Sequential Decision Problems with Multiplicative Loss,'' Signal Processing, vol. 92, issue 4, pp. 890-905, April 2011.

-- S. S. Kozat, A. C. Singer, ``Universal semiconstant portfolios,'' Mathematical Finance, vol. 21, no. 2, pp. 293-311, April 2011.

-- S. S. Kozat, A. C. Singer, ``Universal Constant Rebalanced Portfolios with Switching,'' IEEE Int. Conf. on Acoustic Speech and Signal Processing, pp. 1129-1132, April 2007.

-- S. S. Kozat, A. C. Singer, ``Universal Portfolios for Switching and Side-information,'' IEEE Workshop on Machine Learning for Signal Processing, 2006.

FIGURE: Actual performance of the introduced algorithms while trading in the New York Stock Exchange. The details are provided in our publications.