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Continuous time mean-variance portfolio optimization with piecewise state-dependent risk aversion

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Abstract

In this paper, a continuous time mean-variance portfolio optimization problem is considered within a game theoretic framework, where the risk aversion function is assumed to depend on the current wealth level and the discounted (preset) investment target. We derive the explicit time consistent investment policy, and find that if the current wealth level is less (larger) than the discounted investment target, the future wealth level along the time consistent investment policy is always less (larger) than the discounted investment target.

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Acknowledgments

This work is partially supported by grants of the National Natural Science Foundation of China (Nos. 71201094, 71201173, 71571195), Innovation Project Research Fund of SHUFE (No. CXJJ-2014-463), Program for Changjiang Scholars and Innovative Research Team in SUFE (No. IRT13077), Guangdong Natural Science for Research Team (2014A030312003), Guangdong Natural Science Funds for Distinguished Young Scholar (No. 2015A030306040) and Natural Science Foundation of Guangdong Province of China (No.S2013010011959).

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Authors and Affiliations

  1. School of Statistics and Management, Shanghai Key Laboratory of Financial Information Technology, Shanghai University of Finance and Economics, Shanghai, China

    Xiangyu Cui

  2. School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China

    Lu Xu

  3. Lingnan (University) College, Sun Yat-sen University, Guangzhou, China

    Yan Zeng

Authors
  1. Xiangyu Cui
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  2. Lu Xu
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  3. Yan Zeng
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Correspondence to Yan Zeng.

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Cui, X., Xu, L. & Zeng, Y. Continuous time mean-variance portfolio optimization with piecewise state-dependent risk aversion. Optim Lett 10, 1681–1691 (2016). https://doi.org/10.1007/s11590-015-0970-8

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  • DOI: https://doi.org/10.1007/s11590-015-0970-8

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