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Optimal Investment Strategy With Dividend Paying And Proportional Transaction Costs

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  • CHARLES. I. NKEKI

    (Department of Mathematics, Faculty of Physical Sciences, University of Benin, P. M. B. 1154, Benin City, Edo State, Nigeria)

Abstract

A Markowitz’s mean-variance investment strategy is studied in a market with a stock, a bond, dividend payment and proportional transaction costs. Two control variables, portfolio strategy and dividend are considered in this paper. The control variables are inherent with a finite time horizon. This paper aims at minimizing the investment portfolio risk and maximizing the dividend process of the investment over time subject to portfolio allocation strategy, expected net wealth and investment costs over time. The method of Lagrangian multiplier was adopted. As a result, the optimal portfolio and optimal dividend payment are obtained. We found that the optimal portfolio process depends on the optimal dividend payment over time. Also, obtained in this paper, is the optimal portfolio with no dividend payment. We found that for the investment to achieve high target, more of the fund should be invested in stock and low dividend should be declared. The region of boundedness for stock purchase and stock sale are established. We found that for the investment to break-even, the quantum amount of stock sold must be greater than the quantum amount of stock purchase over time. The efficient frontier of the investment strategy was also obtained.

Suggested Citation

  • Charles. I. Nkeki, 2018. "Optimal Investment Strategy With Dividend Paying And Proportional Transaction Costs," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 13(01), pages 1-17, March.
    • Handle: RePEc:wsi:afexxx:v:13:y:2018:i:01:n:s201049521850001x
    DOI: 10.1142/S201049521850001X
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    References listed on IDEAS

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    1. Harry Markowitz, 1956. "The optimization of a quadratic function subject to linear constraints," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 111-133, March.
    2. Majid Shakhsi-Niaei & Morteza Shiripour & Hamed Shakouri G. & Seyed Hossein Iranmanesh, 2015. "Application of genetic and differential evolution algorithms on selecting portfolios of projects with consideration of interactions and budgetary segmentation," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 22(1), pages 106-128.
    3. Charles I. Nkeki, 2018. "Optimal investment risks management strategies of an economy in a financial crisis," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 1-24, March.
    4. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1851-1872, September.
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