Speedup algorithm: Modified policy iterations

We consider the following m states model without labor as in 0827 and 0903 and 0910:

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.

.

where

.

.

.

with probability matrix:

We also consider the following m states model with labor as in 0828 and 0903:

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.

.

where

and

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.

.

and

.

.

.

where both technology change parameter and form of leisure utility change according

to state. As done before, the probability matrix used here is considered backward and

it is different from transition matrix mentioned later.

The resulting state can be computed by the calculation of each policy function with

each state. We speed up each calculation by modified policy iterations.

When we compute each policy function for each and h( ), we apply modified policy

iterations to speed up. We also combine error bounds.

Technically, we attach option 4 by modifying option 3 and add option 5 to option 1.