Dynamic growth-optimum portfolio choice under risk control

TL;DR

This paper develops a continuous-time mean-risk portfolio optimization model using weighted Value-at-Risk (WVaR) for log-returns, providing analytical solutions and insights into the shape of the efficient frontier.

Contribution

It introduces a novel mean-WVaR criterion for dynamic portfolio choice and derives explicit solutions for optimal wealth and policies under this measure.

Findings

Optimal terminal wealth characterized by concave envelope

Analytical expressions for optimal wealth and portfolio policies

Efficient frontier is a concave curve connecting key portfolios

Abstract

This paper studies a mean-risk portfolio choice problem for log-returns in a continuous-time, complete market. This is a growth-optimal problem with risk control. The risk of log-returns is measured by weighted Value-at-Risk (WVaR), which is a generalization of Value-at-Risk (VaR) and Expected Shortfall (ES). We characterize the optimal terminal wealth up to the concave envelope of a certain function, and obtain analytical expressions for the optimal wealth and portfolio policy when the risk is measured by VaR or ES. In addition, we find that the efficient frontier is a concave curve that connects the minimum-risk portfolio with the growth optimal portfolio, as opposed to the vertical line when WVaR is used on terminal wealth. Our results advocate the use of mean-WVaR criterion for log-returns instead of terminal wealth in dynamic portfolio choice.