Dynamic Mean–Variance Portfolio Optimization with Value-at-Risk Constraint in Continuous Time

Tongyao Wang, Qitong Pan (), Weiping Wu, Jianjun Gao and Ke Zhou
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Tongyao Wang: Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, China
Qitong Pan: School of Economics and Management, Fuzhou University, Fuzhou 350108, China
Weiping Wu: School of Economics and Management, Fuzhou University, Fuzhou 350108, China
Jianjun Gao: School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai 200433, China
Ke Zhou: Business School, Hunan University, Changsha 410082, China

Mathematics, 2024, vol. 12, issue 14, 1-17

Abstract: Recognizing the importance of incorporating different risk measures in the portfolio management model, this paper examines the dynamic mean-risk portfolio optimization problem using both variance and value at risk (VaR) as risk measures. By employing the martingale approach and integrating the quantile optimization technique, we provide a solution framework for this problem. We demonstrate that, under a general market setting, the optimal terminal wealth may exhibit different patterns. When the market parameters are deterministic, we derive the closed-form solution for this problem. Examples are provided to illustrate the solution procedure of our method and demonstrate the benefits of our dynamic portfolio model compared to its static counterpart.

Keywords: dynamic mean–variance portfolio selection; value at risk; stochastic optimization; martingale approach; continuous-time models (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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