Abstract
This paper considers a multi-period mean-variance portfolio selection problem with no shorting constraint. We assume that the sample space is finite, and the possible securities price vector transitions is equivalent to the number of securities. By making use of the embedding technique of Li and Ng (2000), the original nonseparable problem can be solved by introducing an auxiliary problem. After the risk neutral probability is calculated, the auxiliary problem can be solved by using the martingale method of Pliska (1986). Finally, we derive a closed form of the optimal solution to the original constrained problem.
Highlights
Portfolio theory deals with the question of how to find an optimal distribution of the wealth among various assets
This paper extends existing literature by utilizing a martingale approach to solve an optimal portfolio selection problem with no-shorting constraint
Optimal mean-variance multiperiod portfolio selection with no shorting constraints problem is studied in the paper
Summary
Portfolio theory deals with the question of how to find an optimal distribution of the wealth among various assets. Mean-variance analysis and expected utility formulation are two different tools for dealing with portfolio selections. A fundamental basis for portfolio selection in a single period was provided by Markowitz. Under the assumption that short-selling of stocks is not allowed, analytical expression of the mean-variance efficient frontier in single-period portfolio selection was derived by solving a quadratic programming problem in Markowitz (1952) [1]. An analytical solution to the single-period meanvariance problem with assumption that short-selling is allowed is derived in Merton (1972) [2]. A multi-period portfolio selection problem has been studied. This problem is more interesting as investors always invest their wealth in multi
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