习惯形成模型下的退休消费问题
Retirement spending problem under Habit Formation Model
摘要：
本文研究了在习惯形成模型下的终身消费优化问题。我们的工作不同于以往的结果，因为我们纳入了死亡率和养老金收入。由于年龄的影响，消费的终身效用使得问题的时间不均匀。考虑习惯形成意味着增加随机控制问题的维度，因为必须使用额外的变量习惯$\bar c$来跟踪平滑消费。包括外生养老金收入$π$意味着，我们不能依赖于一种缩放变换，以减少在早期的工作中的问题的维度，因此，我们解决它的数值，使用有限差分格式。我们还探讨了消费如何随着时间的推移而变化的习惯，如果退休人员遵循最佳策略。最后，我们回答的问题，是否是合理的年金化的财富在退休时或不通过改变参数，如资产配置$θ$和平滑因子$η$。
英文摘要：
In this paper we consider the problem of optimizing lifetime consumption under a habit formation model. Our work differs from previous results, because we incorporate mortality and pension income. Lifetime utility of consumption makes the problem time inhomogeneous, because of the effect of ageing. Considering habit formation means increasing the dimension of the stochastic control problem, because one must track smoothed-consumption using an additional variable, habit $\bar c$. Including exogenous pension income $π$ means that we cannot rely on a kind of scaling transformation to reduce the dimension of the problem as in earlier work, therefore we solve it numerically, using a finite difference scheme. We also explore how consumption changes over time based on habit if the retiree follows the optimal strategy. Finally, we answer the question of whether it is reasonable to annuitize wealth at the time of retirement or not by varying parameters, such as asset allocation $θ$ and the smoothing factor $η$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
