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Robust Portfolio Optimization with Multi-Factor Stochastic Volatility

Author

Listed:
  • Ben-Zhang Yang

    (Sichuan University)

  • Xiaoping Lu

    (University of Wollongong)

  • Guiyuan Ma

    (The Chinese University of Hong Kong)

  • Song-Ping Zhu

    (University of Wollongong)

Abstract

This paper studies a robust portfolio optimization problem under a multi-factor volatility model. We derive optimal strategies analytically under the worst-case scenario with or without derivative trading in complete and incomplete markets and for assets with jump risk. We extend our study to the case with correlated volatility factors and propose an analytical approximation for the robust optimal strategy. To illustrate the effects of ambiguity, we compare our optimal robust strategy with the strategies that ignore the information of uncertainty, and provide the welfare analysis. We also discuss how derivative trading affects the optimal strategies. Finally, numerical experiments are provided to demonstrate the behavior of the optimal strategy and the utility loss.

Suggested Citation

  • Ben-Zhang Yang & Xiaoping Lu & Guiyuan Ma & Song-Ping Zhu, 2020. "Robust Portfolio Optimization with Multi-Factor Stochastic Volatility," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 264-298, July.
    • Handle: RePEc:spr:joptap:v:186:y:2020:i:1:d:10.1007_s10957-020-01687-w
    DOI: 10.1007/s10957-020-01687-w
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    3. Ying Zhao & Hui Mi & Lixia Xu, 2022. "Robust Optimal Investment Problem with Delay under Heston’s Model," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1271-1296, June.
    4. Wujun Lv & Tao Pang & Xiaobao Xia & Jingzhou Yan, 2023. "Dynamic portfolio choice with uncertain rare-events risk in stock and cryptocurrency markets," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-28, December.
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    6. Ben-Zhang Yang & Xin-Jiang He & Song-Ping Zhu, 2020. "Mean-variance-utility portfolio selection with time and state dependent risk aversion," Papers 2007.06510, arXiv.org, revised Aug 2020.

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