This repository aims to extend EconPDEs.jl to permit jump diffusions in endogenous state variables by applying pseudo-transient continuation to the value function iteration method developed by Li, Wenhao (2020) "Public Liquidity and Financial Crises". The key problem is that with jump diffusions the Hamilton-Jacobi-Bellman equation becomes an integro-differential equation. Li (2020) handles this problem with tempered fixed-point iteration. The method, however, requires log utility for agents. To extend the method for more general preferences and models, I plan to use pseudo-transient relaxation as the proposal method for the next guess of value functions in the tempered fixed-point iteration.
The current plan of development is
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Replicate Li (2020) in Julia. (DONE)
a. Approx. 4 times faster (2s in Julia vs. 8s in MATLAB) on a Macbook Pro.
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Implement basic "Brunnermeier-Sannikov" style model with jumps.
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Rewrite the solution method to apply pseudo-transient continuation. Test with the Brunnermeier-Sannikov model.
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Extend EconPDEs.jl to permit generic problems featuring fixed points.