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Working Paper
Applications of Markov Chain Approximation Methods to Optimal Control Problems in Economics
In this paper we explore some benefits of using the finite-state Markov chain approximation (MCA) method of Kushner and Dupuis (2001) to solve continuous-time optimal control problems in economics. We first show that the implicit finite-difference scheme of Achdou et al. (2022) amounts to a limiting form of the MCA method for a certain choice of approximating chains and policy function iteration for the resulting system of equations. We then illustrate that, relative to the implicit finite-difference approach, using variations of modified policy function iteration to solve income fluctuation ...