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Optimal investment strategy for a DC pension plan with mispricing under the Heston model

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  • Jie Ma
  • Hui Zhao
  • Ximin Rong

Abstract

In this article, we consider the optimal investment problem for a defined contribution (DC) pension plan with mispricing. We assume that the pension funds are allowed to invest in a risk-free asset, a market index, and a risky asset with mispricing, i.e. the prices are inconsistent in different financial markets. Assuming that the price process of the risky asset follows the Heston model, the manager of the pension fund aims to maximize the expected utility for the power utility function of terminal wealth. By applying stochastic control theory, we establish the corresponding Hamilton-Jacobi-Bellman (HJB) equation. And the optimal investment strategy is obtained for the power utility function explicitly. Finally, numerical examples are provided to analyze effects of parameters on the optimal strategy.

Suggested Citation

  • Jie Ma & Hui Zhao & Ximin Rong, 2020. "Optimal investment strategy for a DC pension plan with mispricing under the Heston model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(13), pages 3168-3183, July.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:13:p:3168-3183
    DOI: 10.1080/03610926.2019.1586938
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    Cited by:

    1. Yumo Zhang, 2021. "Dynamic Optimal Mean-Variance Investment with Mispricing in the Family of 4/2 Stochastic Volatility Models," Mathematics, MDPI, vol. 9(18), pages 1-25, September.
    2. 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.
    3. 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.
    4. Wang, Ning & Zhang, Yumo, 2023. "Robust optimal asset-liability management with mispricing and stochastic factor market dynamics," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 251-273.

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