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Optimal investment with S-shaped utility and trading and Value at Risk constraints: An application to defined contribution pension plan

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  • Dong, Yinghui
  • Zheng, Harry

Abstract

In this paper we investigate an optimal investment problem under loss aversion (S-shaped utility) and with trading and Value-at-Risk (VaR) constraints faced by a defined contribution (DC) pension fund manager. We apply the concavification and dual control method to solve the problem and derive the closed-form representation of the optimal terminal wealth in terms of a controlled dual state variable. We propose a simple and effective algorithm for computing the initial dual state value, the Lagrange multiplier and the optimal terminal wealth. Theoretical and numerical results show that the VaR constraint can significantly impact the distribution of the optimal terminal wealth and may greatly reduce the risk of losses in bad economic states due to loss aversion.

Suggested Citation

  • Dong, Yinghui & Zheng, Harry, 2020. "Optimal investment with S-shaped utility and trading and Value at Risk constraints: An application to defined contribution pension plan," European Journal of Operational Research, Elsevier, vol. 281(2), pages 341-356.
    • Handle: RePEc:eee:ejores:v:281:y:2020:i:2:p:341-356
    DOI: 10.1016/j.ejor.2019.08.034
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    3. Xiao Xu, 2020. "The optimal investment strategy of a DC pension plan under deposit loan spread and the O-U process," Papers 2005.10661, arXiv.org.
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    5. Marcos Escobar-Anel & Michel Kschonnek & Rudi Zagst, 2022. "Portfolio optimization: not necessarily concave utility and constraints on wealth and allocation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(1), pages 101-140, February.
    6. Xun Li & Xiang Yu & Qinyi Zhang, 2021. "Optimal consumption with loss aversion and reference to past spending maximum," Papers 2108.02648, arXiv.org, revised Mar 2024.
    7. M. Escobar-Anel & M. Kschonnek & R. Zagst, 2023. "Mind the cap!—constrained portfolio optimisation in Heston's stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 23(12), pages 1793-1813, November.
    8. Guohui Guan & Zongxia Liang & Yi Xia, 2023. "Optimal management of DB pension fund under both underfunded and overfunded cases," Papers 2302.08731, arXiv.org.
    9. Butt, Adam & Khemka, Gaurav & Warren, Geoffrey J., 2022. "Heterogeneity in optimal investment and drawdown strategies in retirement," Pacific-Basin Finance Journal, Elsevier, vol. 74(C).
    10. Guohui Guan & Zongxia Liang & Yi xia, 2021. "Optimal management of DC pension fund under relative performance ratio and VaR constraint," Papers 2103.04352, arXiv.org.
    11. Chen, Zheng & Li, Zhongfei & Zeng, Yan, 2023. "Portfolio choice with illiquid asset for a loss-averse pension fund investor," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 60-83.
    12. Zongxia Liang & Yang Liu & Litian Zhang, 2021. "A Framework of State-dependent Utility Optimization with General Benchmarks," Papers 2101.06675, arXiv.org, revised Dec 2023.
    13. John Armstrong & Damiano Brigo & Alex S. L. Tse, 2020. "The importance of dynamic risk constraints for limited liability operators," Papers 2011.03314, arXiv.org.
    14. Guan, Guohui & Liang, Zongxia & Xia, Yi, 2023. "Optimal management of DC pension fund under the relative performance ratio and VaR constraint," European Journal of Operational Research, Elsevier, vol. 305(2), pages 868-886.
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    18. Christian Dehm & Thai Nguyen & Mitja Stadje, 2020. "Non-concave expected utility optimization with uncertain time horizon," Papers 2005.13831, arXiv.org, revised Oct 2021.
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