Currently, my work focuses on implementing adaptive learning techniques in stochastic continuous-time models.
This setting advantageous as the solution algorithms for these models is fast and yields detailed information about the distribution of key variables.
Works in Progress
Linear Quadratic Methods in Continuous-Time (In progress)
The linear quadratic framework allows for large and complex models of the macroeconomy. This framework has been studied extensively in discrete-time, yet very few papers have explored the continuous-time analogs. I recast the traditional linear quadratic regulator problem in continuous-time and outline solution methods for the dynamic programming problem. I also show that under certain variable transforms and small time intervals, a discrete-time system in this setting will converge to the same solutions as the continuous-time system. Most importantly, I examine adaptive rules in this setting and find convergence to rational expectations equilibria under learning rules with exact discrete data.
Adaptive Learning in a Continuous-Time Setting: Representative Agent Exercises
I examine simple Ramsey models in both discrete and continuous-time settings, then using exact discrete time models that depend on time intervals I demonstrate that the discrete models limit to the continuous-time models. The majority of this paper focuses on stylized learning rules in the continuous-time setting. These stylized learning rules involve updating parameters, but no direct feedback from the model itself. For more information and code from this project visit my github repo.