Speedup algorithm: error bounds

Basic Algorithm for grid in 0723 and 0724:

(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.

(4) Repeat (3) by setting v=v1 for many times or until some criterion is met.

(5) Find the final corresponding value of k as k’ according to the maximum value.

We consider the following model:

where and

Modified algorithm for error bounds:

where

We modify (3) and add the adjustment part to the next.

This adjustment part will converge to zero as the time step goes on.