Dynamic Mean-VaR Portfolio Selection in Continuous Time

27 Pages Posted: 7 Jun 2016

See all articles by Ke Zhou

Ke Zhou

Hunan University - Business School

Jianjun Gao

Shanghai University of Finance and Economics; Shanghai Jiao Tong University

Duan Li

Chinese University of Hong Kong; City University of Hong Kong

Xiangyu Cui

Shanghai University of Finance and Economics - School of Statistics and Management

Date Written: June 5, 2016

Abstract

In the existing literature, the value-at-risk (VaR) is one of the most representative downside risk measures due to its wide spectra of applications in practice. In this paper, we investigate the dynamic mean-VaR portfolio selection formulation, while the state-of-the-art has only witnessed static versions for mean-VaR portfolio selection. Our contributions are two-fold, in both building up a tractable formulation and deriving the corresponding optimal portfolio policy. By imposing a limit funding level on the terminal wealth, we conquer the ill-posedness exhibited in the original dynamic mean-VaR portfolio formulation. To overcome the difficulties arising from the VaR constraint and no bankruptcy constraint, we have combined the martingale approach with the quantile optimization technique in our solution framework such that to derive the optimal portfolio policy. In particular, we have characterized the condition of the existence of the Lagrange multiplier. When the opportunity set of the market setting is deterministic, the portfolio policy becomes analytical. Furthermore, the limit funding level not only enables us to solve the dynamic mean-VaR portfolio selection problem, but also offers a flexibility to tame the aggressiveness of the portfolio policy.

Keywords: Dynamic portfolio selection, Value-at-risk, Quantile Method

JEL Classification: G11, C61

Suggested Citation

Zhou, Ke and Gao, Jianjun and Li, Duan and Cui, Xiangyu, Dynamic Mean-VaR Portfolio Selection in Continuous Time (June 5, 2016). Available at SSRN: https://ssrn.com/abstract=2790440 or http://dx.doi.org/10.2139/ssrn.2790440

Ke Zhou

Hunan University - Business School ( email )

Changsha, Hunan 410082
China

Jianjun Gao

Shanghai University of Finance and Economics ( email )

No. 100 Wudong Road
Shanghai, Shanghai 200433
China

Shanghai Jiao Tong University ( email )

800 Dongchuan Road
Shanghai
China
+86-18201925139 (Phone)
+86 34205004 (Fax)

Duan Li (Contact Author)

Chinese University of Hong Kong ( email )

Shatin, New Territories
Hong Kong

City University of Hong Kong

Tat Chee Avenue
Kowloon Tong
Kowloon
Hong Kong
852 3442 8591 (Phone)

Xiangyu Cui

Shanghai University of Finance and Economics - School of Statistics and Management ( email )

777 Guoding Road
Shanghai, Shanghai 200433
China

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