Asset pricing with dynamic programming

  • Authors:

  • Lars Grüne;Willi Semmler

  • Affiliations:

  • Mathematisches Institut, Fakultät für Mathematik und Physik, Universität Bayreuth, Bayreuth, Germany 95440;Schwartz Center for Economic Policy Analysis, New School, New York, USA and Center for Empirical Macroeconomics, Bielefeld University, Bielefeld, Germany

  • Venue:
  • Computational Economics
  • Year:
  • 2007

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Abstract

The study of asset price characteristics of stochastic growth models such as the risk-free 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), Journal of Economic Theory, 4, 479---513 and Brock (1979), Part I: The growth model (pp. 165---190). New York: Academic Press; The economies of information and uncertainty (pp. 165---192). Chicago: University of Chicago Press. (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 dynamic programming method with adaptive grid scheme to compute the above mentioned asset price characteristics. We show that our method is very suitable to be used as solution technique for such models with more complicated decision structure.