Stochastic Models for Portfolio Management with Minimum Transaction Lots

In this paper, we consider the problem of a decision maker who is concerned with the management of a portfolio over a finite horizon. The portfolio optimization problem involves portfolio rebalancing decisions in response to new information on market future prices of the risky assets. Rebalancing decisions are manifested in the revision of holdings through sales and purchases of assets. We assume that the assets are sufficiently liquid that market impacts can be neglected. Usually, portfolio selection problems are solved with quadratic or linear programming models. In the real life applications, each asset usually has its minimum transaction lot. Methods considering minimum transaction lots were developed based on some linear portfolio optimization models. In this paper, we study the minimum transaction lot problem in portfolio optimization based on Markowitz’ model, which is probably the most well-known and widely used. Based on Markowitz’ model, this study presents three possible models for portfolio selection problems with minimum transaction lots and discuss a twoparameter penalty algorithm to obtain the optimal solutions (decisions) for the portfolio problems.