Risk and Return in a Dynamic Asset Pricing Model

In this study we combine the dynamic programming method with the projection methods for solving stochastic growth models. One of the inconveniences of Judd's projection technique is that finding a good initial guess is not that easy or it is time costly especially when the dimensionality of the problem is high. Secondly, there is no theoretical assurance that projection technique converges to the true policy function. First we use the dynamic programming method to obtain an approximate solution for the policy function. Since the approximate solution is in the vicinity of the true solution, we use those coefficients as the initial guess for the projection method. Then we use Judd's projection method to find an exact solution for the policy function. Once we find the exact solution for the policy function we check whether or not projection method converged to the true policy function. We do that by using the dynamic programming method to test whether the policy function satisfies the Bellman equation.