Research on business fluctuations caused by discrete choice problems

本研究旨在探讨离散选择问题与企业波动之间的关系。离散选择问题是重要的，因为许多产品在现实中是不可分割的。在这项研究中，已经表明，在个人层面上，离散选择问题的结果是复杂的动态。这个结果的一个更精确的陈述如下：在相当一般的条件下，确定性无限时域离散选择问题的最优路径几乎从不收敛到一个稳定状态或一个循环。在技术方面，我采用了将无限时域优化问题看作无限维空间中的优化问题的方法，而不是动态规划。通过比较状态空间和最优路径空间，我已经表明，最优路径几乎总是表现出复杂的动态。我正在准备一份基于上述结果的论文，准备在期刊上发表。

The purpose of this research is to study the relationship between discrete choice problems and business fluctuations. Discrete choice problems are important since many products in reality are indivisible.In this research, it has been shown that at the individual level, discrete choice problems result in complex dynamics. A more precise statement of this result is as follows: Under quite general conditions, the optimal paths of deterministic infinite-horizon discrete-choice problems almost never converge to a steady state or a cycle.In terms of techniques, in stead of dynamic programming, I have employed the approach of viewing an infinite horizon optimization problem as an optimization problem in an infinite dimensional space. By comparing the state space and the space of optimal paths, I have shown that optimal paths almost always exhibit complex dynamics.I am in the process of preparing a paper based on the above result for publication in a journal.