OPTIMAL INVESTMENT STRATEGY WITH DIVIDEND PAYING AND PROPORTIONAL TRANSACTION COSTS

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.