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Asset pricing with dynamic programming

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  • Lars Grüne

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  • Willi Semmler

    ()

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. Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • Lars Grüne & Willi Semmler, 2007. "Asset pricing with dynamic programming," Computational Economics, Springer;Society for Computational Economics, vol. 29(3), pages 233-265, May.
  • Handle: RePEc:kap:compec:v:29:y:2007:i:3:p:233-265 DOI: 10.1007/s10614-006-9063-1
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Grüne, Lars & Semmler, Willi, 2008. "Asset pricing with loss aversion," Journal of Economic Dynamics and Control, Elsevier, vol. 32(10), pages 3253-3274, October.
    2. Zhang, Wenlang & Semmler, Willi, 2009. "Prospect theory for stock markets: Empirical evidence with time-series data," Journal of Economic Behavior & Organization, Elsevier, vol. 72(3), pages 835-849, December.
    3. Stefan Mittnik & Willi Semmler, 2011. "The Instability of the Banking Sector and Macrodynamics: Theory and Empirics," DEGIT Conference Papers c016_080, DEGIT, Dynamics, Economic Growth, and International Trade.

    More about this item

    Keywords

    Stochastic growth models; Asset pricing; Stochastic dynamic programming; Adaptive grid; C60; C61; C63; D90; G12;

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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