论文标题
习惯形成模型下的退休支出问题
Retirement spending problem under Habit Formation Model
论文作者
论文摘要
在本文中，我们考虑了在习惯形成模型下优化终生消费的问题。我们的工作与以前的结果不同，因为我们纳入了死亡率和养老金收入。由于衰老的影响，消费的终身用途使问题的时间不均匀。考虑习惯形成意味着增加随机控制问题的维度，因为必须使用附加变量，习惯$ \ bar c $跟踪平滑消费。包括外在的养老金收入$π$意味着我们不能像早期工作一样依靠一种缩放变换来减少问题的维度，因此，我们使用有限的差异方案来数字解决。如果退休人员遵循最佳策略，我们还探讨了根据习惯随时间变化的消费如何变化。最后，我们回答了一个问题，即通过不同的参数（例如资产分配$θ$和平滑因子$η$）在退休时是否合理地使财富变成平等。
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 $η$.
