论文标题
最佳投资，异质消费和最佳退休时间
Optimal Investment, Heterogeneous Consumption and Best Time for Retirement
论文作者
论文摘要
本文研究了基本和奢侈品的异质消费以及退休时间的最佳投资和消费问题。奢侈品的实用程序不一定是凹面功能。证明，在财富很小的时候只能消耗基本商品，在财富中间时消耗基本商品并节省几乎所有的奢侈品，而当财富大时消费，那么当财富很小时消耗基本商品并节省了几乎所有的奢侈品。最佳的退休政策被证明是普遍的，因为所有个人都应以相同水平的边际效用退休，而边际效用仅取决于收入，劳动成本，折扣因子和市场参数，而不是普遍的，因为所有个人都可以实现与不同效用和财富相同的边际公用事业。还表明，如果边际劳动成本增加的速度比收入的速度快，则个人更喜欢随着时间的流逝而退休。用于分析该问题的主要工具来自PDE和随机控制理论，包括变异不平等和双重变换。我们最终对特色模型参数进行了仿真分析，以通过提供其数字来调查实际和经济影响。
This paper studies an optimal investment and consumption problem with heterogeneous consumption of basic and luxury goods, together with the choice of time for retirement. The utility for luxury goods is not necessarily a concave function. The optimal heterogeneous consumption strategies for a class of non-homothetic utility maximizer are shown to consume only basic goods when the wealth is small, to consume basic goods and make savings when the wealth is intermediate, and to consume almost all in luxury goods when the wealth is large. The optimal retirement policy is shown to be both universal, in the sense that all individuals should retire at the same level of marginal utility that is determined only by income, labor cost, discount factor as well as market parameters, and not universal, in the sense that all individuals can achieve the same marginal utility with different utility and wealth. It is also shown that individuals prefer to retire as time goes by if the marginal labor cost increases faster than that of income. The main tools used in analyzing the problem are from PDE and stochastic control theory including variational inequality and dual transformation. We finally conduct the simulation analysis for the featured model parameters to investigate practical and economic implications by providing their figures.
