II. Module 4 Homework [practice]: Equity Premium and Macroeconomics

Due No due date
Points 18
Questions 9
Time Limit None
Allowed Attempts 2

Instructions

Write the continuous time habit model with utility

$LaTeX: \frac{1}{1-\gamma}E\int_{t=0}^\infty e^{-\rho t} (C_t - X_t)^ {1-\gamma} dt$ and
$LaTeX: ds_t = (1-\phi)(\bar{s}-s_t ) dt + \lambda(s_t)(dc_t - g dt)$

where

$LaTeX: dc_t = g dt + \sigma dz_t$
$LaTeX: s_t = \log\frac{C_t - X_t} {C_t}$

(This is slightly different from the continuous time model I wrote in the lecture overheads notes. Use this one. I made the notation more similar to the paper here.)

We'll redo some of the simple calculations of the paper in continuous time. This gives you a review of the model and some practice
with continuous time.

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