<p>This paper investigates the optimal investment and benefit adjustment problem for a collective hybrid pension plan in the presence of a longevity trend. The mortality hazard rate is assumed to depend on both age and time, which extends Makeham’s law and captures the longevity trend in residents’ life expectancy. The contribution rate is set as a predetermined proportion of pension wealth, while the benefit payment is adjusted according to the level of pension wealth. The pension fund is allowed to invest in a risk-free asset and a risky asset whose price process satisfies the constant elasticity of variance (CEV) model. By applying dynamic programming approach, we derive the corresponding Hamilton–Jacobi–Bellman (HJB) equation and obtain the optimal investment and benefit strategies for constant absolute risk aversion (CARA) and constant relative risk aversion (CRRA) utility functions, respectively. Finally, numerical examples are provided to illustrate the effects of the parameters on the optimal strategies. The results show that longevity risk affects only the optimal benefit strategy under the CARA utility function, whereas the longevity trend influences both the optimal benefit and investment strategies under the CRRA utility function.</p>

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Optimal investment and benefit adjustment problem for a hybrid pension plan with longevity trend under the CEV model

  • Yufang Zhang,
  • Ximin Rong,
  • Hui Zhao

摘要

This paper investigates the optimal investment and benefit adjustment problem for a collective hybrid pension plan in the presence of a longevity trend. The mortality hazard rate is assumed to depend on both age and time, which extends Makeham’s law and captures the longevity trend in residents’ life expectancy. The contribution rate is set as a predetermined proportion of pension wealth, while the benefit payment is adjusted according to the level of pension wealth. The pension fund is allowed to invest in a risk-free asset and a risky asset whose price process satisfies the constant elasticity of variance (CEV) model. By applying dynamic programming approach, we derive the corresponding Hamilton–Jacobi–Bellman (HJB) equation and obtain the optimal investment and benefit strategies for constant absolute risk aversion (CARA) and constant relative risk aversion (CRRA) utility functions, respectively. Finally, numerical examples are provided to illustrate the effects of the parameters on the optimal strategies. The results show that longevity risk affects only the optimal benefit strategy under the CARA utility function, whereas the longevity trend influences both the optimal benefit and investment strategies under the CRRA utility function.