Reading paper and techniques together

[bigbigben]

I know it is not really about dynare, but this is the best outlet I can find to discuss some questions, especially some kind of technical issues. The topic in my mind is the series of papers by Mackus Brunnermeier and Yuliy Sannikov, including "A Macroeconomic Model with Financial Sector", "The I Theory of Money" and the recent survey, "Macro, Money and Finance: A Continuous Time Approach". I like the first paper very much, since it offers a simple and elegant way to have a DSGE model with multiple distinctive equilibria (The "animal spirit" literature usually get a continuum of equilibria). The second paper's idea is also intriguing: the main function of money is to help offload the idiosyncratic shocks. Even it may not be new to students following the search literature, it offers a simple and tractable alternative. The survey paper tries to summarize the main insight and techniques used in their models.

That being said, there are several gaps I need to fill to fully appreciate their work, and here is an incomplete list of them:

1. The stochastic Hamiltonian
I know that the HJB equation is a more conventional way to solve stochastic control problems. The stochastic Hamiltonian approach used in the third paper (Starting from page 19, and titled as Stochastic Maximum Principle) seems to be more similar to the Hamiltonian approach in deterministic case, which is simpler than HJB. Can anyone give me a good reference on this approach?

2. In the section "A simple Monetary Model", there are a few statements I do not quite understand.
i. Given the return drM and drK on money and capital, the only two assets traded in this economy, all agents have exposure sigma*dZ to aggregate risk.
Shouldn't it be the case that entrepreneurs have more exposure to the aggregate risk than households? What is the mechanism that leads both entrepreneurs and households to have the same risk expsure?


Above are just a few questions with regard to the topic. I hope there are some one with common interest there. I would happily to share what I know and we may work out those issues together and possibly leads to some research projects.

[Card]

Hello bigbigben,

I was searching the web for related topics and accidentally found your post. I am working right now on the paper "The I Theory of Money" and confronted with the same problems as you are. My objective is to understand the "I Theory of Money" and be abel to derive all equations. I am happy to share my derivations and intuition with you. Maybe we can exchange some ideas and discuss those papers.

What is the best way to get in touch?

I am looking forward to your reply.

Best regards
Card

[bigbigben]

Hi, Cards:

For sure, we can discuss on the forum if you want and others don't mind. I also send you a private message with my contact.