2021/12/29 by Pengyu Wei, Wei, Pengyu, Zuo Quan Xu +1
Decision Sciences · Economics, Econometrics and Finance · #FOS: Economics and business #Financial Markets and Investment Strategies #Mathematical Finance (q-fin.MF) #Portfolio Management (q-fin.PM) #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2112.14451
openalex publication_date 2021/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.