Speedup algorithm: policy iterations

We approximate the continuous random model without labor:

by switching model with infinite many states in order:

.

.

.

where

.

.

.

for many states.

We calculate each policy function for each as it is set like:

independently for each i and calculate the next index number.

The random process can be

for as before.

When we compute each policy function for each, we apply policy iterations.

Random behavior of

The corresponding behavior of capital

where we can find that these two movements are a little bit different

when we magnify the pictures.