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Working Paper
Applications of Markov Chain Approximation Methods to Optimal Control Problems in Economics
In this paper we explore some of the benefits of using the finite-state Markov chain approximation (MCA) method of Kushner and Dupuis (2001) to solve continuous-time optimal control problems. We first show that the implicit finite-difference scheme of Achdou et al. (2017) 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 the benefits of departing from policy function iteration by showing that using variations of modified policy function iteration to solve income ...
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 ...
Working Paper
The Art of Temporal Approximation An Investigation into Numerical Solutions to Discrete and Continuous-Time Problems in Economics
A recent literature within quantitative macroeconomics has advocated the use of continuous-time methods for dynamic programming problems. In this paper we explore the relative merits of continuous-time and discrete-time methods within the context of stationary and nonstationary income fluctuation problems. For stationary problems in two dimensions, the continuous-time approach is both more stable and typically faster than the discrete-time approach for any given level of accuracy. In contrast, for convex lifecycle problems (in which age or time enters explicitly), simply iterating backwards ...