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Mean–Variance Portfolio Choice: Quadratic Partial Hedging

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  • Jianming Xia

Abstract

In this paper we investigate the problem of mean–variance portfolio choice with bankruptcy prohibition. For incomplete markets with continuous assets' price processes and for complete markets, it is shown that the mean–variance efficient portfolios can be expressed as the optimal strategies of partial hedging for quadratic loss function. Thus, mean–variance portfolio choice, in these cases, can be viewed as expected utility maximization with non‐negative marginal utility.

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  • Jianming Xia, 2005. "Mean–Variance Portfolio Choice: Quadratic Partial Hedging," Mathematical Finance, Wiley Blackwell, vol. 15(3), pages 533-538, July.
    • Handle: RePEc:bla:mathfi:v:15:y:2005:i:3:p:533-538
    DOI: 10.1111/j.1467-9965.2005.00231.x
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    Cited by:

    1. Fenghui Yu & Wai-Ki Ching & Chufang Wu & Jia-Wen Gu, 2023. "Optimal Pairs Trading Strategies: A Stochastic Mean–Variance Approach," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 36-55, January.
    2. Shuzhen Yang, 2019. "Multi-time state mean-variance model in continuous time," Papers 1912.01793, arXiv.org.
    3. Tomas Björk & Agatha Murgoci & Xun Yu Zhou, 2014. "Mean–Variance Portfolio Optimization With State-Dependent Risk Aversion," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 1-24, January.
    4. Shuzhen Yang, 2019. "A varying terminal time mean-variance model," Papers 1909.13102, arXiv.org, revised Jan 2020.
    5. Wong, K.C. & Yam, S.C.P. & Zeng, J., 2019. "Mean-risk portfolio management with bankruptcy prohibition," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 153-172.
    6. Chen, Binbin & Huang, Shih-Feng & Pan, Guangming, 2015. "High dimensional mean–variance optimization through factor analysis," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 140-159.
    7. Min Dai & Zuo Quan Xu & Xun Yu Zhou, 2009. "Continuous-Time Markowitz's Model with Transaction Costs," Papers 0906.0678, arXiv.org.
    8. De Gennaro Aquino, Luca & Sornette, Didier & Strub, Moris S., 2023. "Portfolio selection with exploration of new investment assets," European Journal of Operational Research, Elsevier, vol. 310(2), pages 773-792.
    9. Xun Li & Xun Yu Zhou, 2007. "Continuous-time mean-variance efficiency: the 80% rule," Papers math/0702249, arXiv.org.
    10. Chi Kin Lam & Yuhong Xu & Guosheng Yin, 2016. "Dynamic portfolio selection without risk-free assets," Papers 1602.04975, arXiv.org.
    11. Bai, Zhidong & Liu, Huixia & Wong, Wing-Keung, 2016. "Making Markowitz's Portfolio Optimization Theory Practically Useful," MPRA Paper 74360, University Library of Munich, Germany.
    12. Lin Chen & Xun Yu Zhou, 2022. "Naive Markowitz Policies," Papers 2212.07516, arXiv.org.
    13. Chonghu Guan & Xiaomin Shi & Zuo Quan Xu, 2022. "Continuous-time Markowitz's mean-variance model under different borrowing and saving rates," Papers 2201.00914, arXiv.org, revised May 2023.
    14. Shuzhen Yang, 2020. "Discrete time multi-period mean-variance model: Bellman type strategy and Empirical analysis," Papers 2011.10966, arXiv.org.
    15. Chonghu Guan & Xiaomin Shi & Zuo Quan Xu, 2023. "Continuous-Time Markowitz’s Mean-Variance Model Under Different Borrowing and Saving Rates," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 167-208, October.

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