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<p>This paper investigates a robust optimal strategy of the target benefit pension (TBP) plan considering inflation risk and model uncertainty under the 4/2 stochastic volatility model. The plan members’ contributions are pre-determined, the pension payments depend on the plan’s financial situation, and the risk of this plan is shared between different generations. Assume that the fund manager, who is ambiguity-averse induced by model uncertainty, can invest the pension wealth in a financial market consisting of a risk-free asset, an inflation-indexed bond and a stock, where the inflation-indexed bond is used to hedge the inflation risk and the price process of the stock is driven by the 4/2 stochastic volatility model. In addition, the wage is considered to be stochastic. With the objective of minimizing benefit risk and discontinuity risk, the extended Hamilton–Jacobi–Bellman (HJB) equation is developed to obtain explicit solutions for the robust optimal investment and benefit payment adjustment strategy. Moreover, two degenerate cases are considered in this paper. Finally, the results obtained are illustrated by numerical examples.</p>

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Robust Optimal Strategy for Target Benefit Pension Plans with Inflation Risk and Model Uncertainty Under 4/2 Stochastic Volatility Model

  • 期刊论文

  • 发表日期：

    2025年12月8日

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  • Li-Tao Wang,
  • Hao Chang

摘要

This paper investigates a robust optimal strategy of the target benefit pension (TBP) plan considering inflation risk and model uncertainty under the 4/2 stochastic volatility model. The plan members’ contributions are pre-determined, the pension payments depend on the plan’s financial situation, and the risk of this plan is shared between different generations. Assume that the fund manager, who is ambiguity-averse induced by model uncertainty, can invest the pension wealth in a financial market consisting of a risk-free asset, an inflation-indexed bond and a stock, where the inflation-indexed bond is used to hedge the inflation risk and the price process of the stock is driven by the 4/2 stochastic volatility model. In addition, the wage is considered to be stochastic. With the objective of minimizing benefit risk and discontinuity risk, the extended Hamilton–Jacobi–Bellman (HJB) equation is developed to obtain explicit solutions for the robust optimal investment and benefit payment adjustment strategy. Moreover, two degenerate cases are considered in this paper. Finally, the results obtained are illustrated by numerical examples.