<p>In this paper, we study the stochastic optimal control problem of the hybrid pension plans under a dynamic foundation. The fund manager controls contribution and benefit adjustment rates, as well as the asset allocation policy, aiming to minimize the costs of discontinuity risk under habitual persistence and the unsustainable risk caused by fund gap. Utilizing the Dynamic Programming Principle and the Hamilton–Jacobi–Bellman equation, we derive explicit optimal adjustment policies and optimal asset allocation policy. We validate the optimality of the solution in the verification theorem. The numerical results show that the initial habitual levels of the adjustment rates have decisive impacts. When the initial adjustment policy is consistent in reducing the fund gap, the adjustment rates are relatively stable. On the contrary, the adjustment magnitude could be large and the investment risk may be unacceptably high. Besides, the adjustment welfare losses are mainly undertaken by the group that has consistent initial policy. Therefore, the economy needs to design forward-looking adjustment policies to ensure that the contribution and benefit rates are within a reasonable scope, as well as prevent a certain group from bearing unfair welfare losses.</p>

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Dynamic optimal adjustment policies of hybrid pension plans under habitual persistence

  • Lin He,
  • Yuting Jia,
  • Zongxia Liang,
  • Sheng Wang

摘要

In this paper, we study the stochastic optimal control problem of the hybrid pension plans under a dynamic foundation. The fund manager controls contribution and benefit adjustment rates, as well as the asset allocation policy, aiming to minimize the costs of discontinuity risk under habitual persistence and the unsustainable risk caused by fund gap. Utilizing the Dynamic Programming Principle and the Hamilton–Jacobi–Bellman equation, we derive explicit optimal adjustment policies and optimal asset allocation policy. We validate the optimality of the solution in the verification theorem. The numerical results show that the initial habitual levels of the adjustment rates have decisive impacts. When the initial adjustment policy is consistent in reducing the fund gap, the adjustment rates are relatively stable. On the contrary, the adjustment magnitude could be large and the investment risk may be unacceptably high. Besides, the adjustment welfare losses are mainly undertaken by the group that has consistent initial policy. Therefore, the economy needs to design forward-looking adjustment policies to ensure that the contribution and benefit rates are within a reasonable scope, as well as prevent a certain group from bearing unfair welfare losses.