Asset Pricing with Dynamic Programming

The study of asset price characteristics of stochastic growth models such as the riskfree interest rate, equity premium and the Sharpe-ratio has been limited by the lack of global and accurate methods to solve dynamic optimization models. In this paper a stochastic version of a dynamic programming method with adaptive grid scheme is applied to compute the asset price characteristics of a stochastic growth model. The stochastic growth model is of the type as developed by Brock and Mirman (1972) and Brock (1979, 1982). It has become the baseline model in the stochastic dynamic general equilibrium literature. In a first step, in order to test our procedure, it is applied to this basic stochastic growth model for which the optimal consumption and asset prices can analytically be computed. Since, as shown, our method produces only negligible errors, as compared to the analytical solution, in a second step, we apply it to more elaborate stochastic growth models with adjustment costs and habit formation. In the latter model preferences are not time separable and past consumption acts as a constraint on current consumption. This model gives rise to an additional state variable. We here too apply our stochastic version of a ∗A version of this paper has been presented at the Conference on Computation in Economics and Finance, Washington, D.C., June 2005, a Workshop at Chuo University, Tokyo, September 2005, and at a Seminar of the German Bundesbank, June 2006. We want to thank the audience for comments. We are also grateful for extensive comments from a referee.