带有通胀风险的退休后最优投资-年金化时刻决策

研究了带通货膨胀的确定缴费养老计划退休后最优投资-年金化决策。假设通货膨胀过程是一个随机过程,建立了真实财富的波动过程。先相对固定年金化时刻,采取目标定位型模型,预设未来各时期的投资目标,利用贝尔曼优化原理,得到从退休时刻到相对固定年金化时刻之间的最优投资策略。接着建立了最优年金化时刻的评估标准,最优的年金化时刻使得年金化前后的累加消费折现均值得到最大。证明了在随机通货膨胀的假设下,传统的自然投资目标不存在;当随机通胀过程退化到确定过程时,求出了自然投资目标的显式表达式,并且在这两种情况下,分析了通胀情况对最优投资策略的影响。最后利用数值分析手段, 研究了通货膨胀、风险偏好、折现率对最优年金化时刻的影响。

Optimal Investment and Timing of Annuitization Post Retirement with Inflation Risk

In the context of a defined contribution pension plan in the de-cumulation phase, this paper studies the optimal strategies of investment and timing of annuitization with inflation risk. The inflation process is assumed to be stochastic and then the real wealth process is set up. The timing of annuitization is first relatively fixed and the investment targets at each period are pre-determined by adopting the target-based model. By using Bellman’s principle of optimality, the optimal investment strategies from the retirement time to the relatively fixed annuitization time are obtained. Thus, the evaluation criteria of the optimal timing of annuity purchase is established which maximizes the accumulated expectations of the consumption before and after the annuitization time. Under the assumption of a stochastic inflation process, the traditional natural targets are proved not to exist. However, when the stochastic inflation process is reduced to be deterministic, the natural targets are derived. Furthermore, in these two cases, the effects of the inflation on the optimal investment strategies are analyzed. Finally, the effects of the inflation, risk preference and discount rate on the timing of annuity purchase are studied by numerical simulation.