Recall the algorithm for a single policy function as in 1119 in the following:
(1) Set a grid consisting of k and k' columnwise and rowwise respectively.
(2) Calculate utility for consumption as U using the grid matrix above.
(3) Starting from a certain v, update v1=U+beta*v so as to maximize v1.
(a) Find the corresponding k’ from (3) in value function iterations.
(b) Calculate utility from k and k’ as r.
(c) Find parameters for f( ) in f1(k)=U+beta*f(k) when f1(k)=k(k) and calculate vp=f(k) with the parameters we get.
(d) Repeat the whole thing by setting vp=vp1 until some criterion is met.
(4) Repeat (3) by setting v=v1 for many times.
(5) Find the final corresponding value of k as k' according to the maximum value.
Now we consider the transition matrix P(tm in the program) and we set
v1=U+beta*P*v
and approximate it as:
f1(k)=U+beta*P*f(k).
Given U=r calculated from k and k’ for each parameter set, we need to solve n x dim of
values in value functions.
Therefore, we have (# of parameter in f(k) for a single function) x dim of parameters
that are simultaneously solved.
It is very difficult for us to compute parameters for f(k) in Newton method and others.