Discretizing nonlinear, non-Gaussian Markov processes with exact conditional moments

• 成果类型: Article
• 署名作者: Farmer, Leland E.; Toda, Alexis Akira
• 署名单位: University of California System; University of California San Diego
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7331
• DOI: 10.3982/QE737
• 发表日期: 2017
• 页码: 651-683
• 关键词: Asset pricing models; Duality; Kullback-Leibler information; numerical methods; solution accuracy

摘要

Approximating stochastic processes by finite-state Markov chains is useful for reducing computational complexity when solving dynamic economic models. We provide a new method for accurately discretizing general Markov processes by matching low order moments of the conditional distributions using maximum entropy. In contrast to existing methods, our approach is not limited to linear Gaussian autoregressive processes. We apply our method to numerically solve asset pricing models with various underlying stochastic processes for the fundamentals, including a rare disasters model. Our method outperforms the solution accuracy of existing methods by orders of magnitude, while drastically simplifying the solution algorithm. The performance of our method is robust to parameters such as the number of grid points and the persistence of the process.