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Optimal Management of DC Pension Plan with Inflation Risk and Tail VaR Constraint

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  • Hui Mi
  • Zuo Quan Xu
  • Dongfang Yang

Abstract

This paper investigates an optimal investment problem under the tail Value at Risk (tail VaR, also known as expected shortfall, conditional VaR, average VaR) and portfolio insurance constraints confronted by a defined-contribution pension member. The member's aim is to maximize the expected utility from the terminal wealth exceeding the minimum guarantee by investing his wealth in a cash bond, an inflation-linked bond and a stock. Due to the presence of the tail VaR constraint, the problem cannot be tackled by standard control tools. We apply the Lagrange method along with quantile optimization techniques to solve the problem. Through delicate analysis, the optimal investment output in closed-form and optimal investment strategy are derived. A numerical analysis is also provided to show how the constraints impact the optimal investment output and strategy.

Suggested Citation

  • Hui Mi & Zuo Quan Xu & Dongfang Yang, 2023. "Optimal Management of DC Pension Plan with Inflation Risk and Tail VaR Constraint," Papers 2309.01936, arXiv.org.
    • Handle: RePEc:arx:papers:2309.01936
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    References listed on IDEAS

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    1. Chen, Zheng & Li, Zhongfei & Zeng, Yan & Sun, Jingyun, 2017. "Asset allocation under loss aversion and minimum performance constraint in a DC pension plan with inflation risk," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 137-150.
    2. Mi, Hui & Xu, Zuo Quan, 2023. "Optimal portfolio selection with VaR and portfolio insurance constraints under rank-dependent expected utility theory," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 82-105.
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