Building up `continuous_time_methods`

[chiyahn]

The goal is to post up a few notes and codes in continuous_time_methods to gradually build up tutorials to be uploaded in PDERoadmap or a dedicated repository. I recommend building up a separate branch and merging it later to master rather than working with master directly. Also, try Weave.jl rather than jupyter notebook for robust replication and version control.

Feel free to edit and add on this issue to keep track of the progress -- reviews are also welcome:

@ajozefiak

@chiyahn

Notes on continuous time methods in macroeconomics (currently working on #95)

Notes I have been working on while following Ben Moll's lecture slides. I'll add up some Julia codes to replicate examples. In particular, notebooks on

• HJB for neoclassical growth models
• HJB for neoclassical growth models, with stochastic k (extend the model as well)
  - [ ] RBC model with linear production function and log-utility
• HJB for Huggett economy -- note that there's an extra borrowing constraint that makes the model slightly more complex

There's a similar code in PDERoadmap repo: https://github.com/JuliaDiffEq/PDERoadmap/blob/master/operator_examples/simple_stationary_HJBE_reflecting.jl

Julia replication for Achdou et al. (2017)

Once the notes from Moll's are complete, I'll be working on replicating codes for Achdou et al. (2017). In particular, focusing on

• continuous-time Huggett Model
• continuous-time Aiyagari Model

Notes on SDE

There are notes I wrote over the last summer based on Oksendal's SDE textbook. They are kind of rough but should be a good resource for reference. I'll post it up here in the repo after some cleanup and adding some details on diffusion process

Notes for PDERoadmap

• Notes for differential operators on irregular grids by basis matrices (Resolved by Add notes on differential operators on irregular grids #94)

Reference

• HJBE and Fokker-Planck (to be added in notebook): https://terrytao.wordpress.com/2010/01/07/mean-field-equations/
• Note by @chiyahn: https://github.com/chiyahn/notes/blob/master/macro/distributional-macro.pdf