Continuous-Time Mean-Variance Portfolio Selection under the CEV Process

Hui-Qiang Ma

doi:10.1155/2014/363046

Abstract

We consider a continuous-time mean-variance portfolio selection model when stock price follows the constant elasticity of variance (CEV) process. The aim of this paper is to derive an optimal portfolio strategy and the efficient frontier. The mean-variance portfolio selection problem is formulated as a linearly constrained convex program problem. By employing the Lagrange multiplier method and stochastic optimal control theory, we obtain the optimal portfolio strategy and mean-variance efficient frontier analytically. The results show that the mean-variance efficient frontier is still a parabola in the mean-variance plane, and the optimal strategies depend not only on the total wealth but also on the stock price. Moreover, some numerical examples are given to analyze the sensitivity of the efficient frontier with respect to the elasticity parameter and to illustrate the results presented in this paper. The numerical results show that the price of risk decreases as the elasticity coefficient increases.

Highlights

The classical mean-variance portfolio selection model, which was first proposed by Markowitz [1], is to minimize the variance of the terminal wealth subject to archiving a given mean return level in a single-period investment
We employ the CEV process to describe the dynamic evolution of the stock price in the mean-variance portfolio selection problem
The results in this paper show that the mean-variance efficient frontier is still a parabola in the mean-variance plane and the optimal strategies are not independent of the stock price

Summary

Introduction

The classical mean-variance portfolio selection model, which was first proposed by Markowitz [1], is to minimize the variance of the terminal wealth subject to archiving a given mean return level in a single-period investment. By exploiting the stochastic control theory, there has been a series of papers discussing the continuous-time mean-variance portfolio selection problem in different markets (see [8,9,10,11,12,13,14] and the references therein). We assume that the stock price follows the CEV process and try to find a mean-variance optimal portfolio strategy and efficient frontier. The results in this paper show that the efficient frontier is still of a perfect square and the optimal portfolio strategy depends on the total wealth and on the stock price.

Problem Formulation

Solutions to the Unconstrained Problem

Efficient Portfolios and Efficient Frontier

Numerical Analysis

Conclusion