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Solving nonlinear stochastic optimal control problems using evolutionary heuristic optimization

Author

Listed:
  • Ivan Savin

    (Faculty of Economics and Business Administration, Friedrich Schiller University Jena, and Chair for Econometrics and Statistics, Graduate School of Economics and Management, Ural Federal University)

  • Dmitri Blueschke

    (University of Klagenfurt)

Abstract

Policy makers constantly face optimal control problems: what controls allow to achieve certain targets in, e.g., GDP growth or inflation? Conventionally this is done by applying certain linear-quadratic optimization algorithms to dynamic econometric models. Several algorithms extend this baseline framework to nonlinear stochastic problems. However, those algorithms are limited in a variety of ways including, most importantly, restriction to local best solutions only and the symmetry of objective function. In Blueschke et al. (2013a) a new flexible optimization method based on Differential Evolution is suggested. It allows to lift these limitations and achieve better approximations of the policy targets, but is designed to deterministic problems only. This study extends the methodology by dealing with stochastic problems in two different ways: applying extreme event analysis and by minimizing the median objective value. Thus, this research is aimed to broaden the range of decision support information used by policy makers in choosing optimal strategy under much more realistic conditions.

Suggested Citation

  • Ivan Savin & Dmitri Blueschke, 2013. "Solving nonlinear stochastic optimal control problems using evolutionary heuristic optimization," Jena Economics Research Papers 2013-051, Friedrich-Schiller-University Jena.
    • Handle: RePEc:jrp:jrpwrp:2013-051
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    File URL: https://oweb.b67.uni-jena.de/Papers/jerp2013/wp_2013_051.pdf
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    References listed on IDEAS

    as
    1. Lyra, M. & Paha, J. & Paterlini, S. & Winker, P., 2010. "Optimization heuristics for determining internal rating grading scales," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2693-2706, November.
    2. Blueschke-Nikolaeva, V. & Blueschke, D. & Neck, R., 2012. "Optimal control of nonlinear dynamic econometric models: An algorithm and an application," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3230-3240.
    3. Blueschke, D. & Blueschke-Nikolaeva, V. & Savin, I., 2013. "New insights into optimal control of nonlinear dynamic econometric models: Application of a heuristic approach," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 821-837.
    4. Benigno, Pierpaolo & Woodford, Michael, 2012. "Linear-quadratic approximation of optimal policy problems," Journal of Economic Theory, Elsevier, vol. 147(1), pages 1-42.
    5. MacRae, Elizabeth Chase, 1975. "An Adaptive Learning Rule for Multiperiod Decision Problems," Econometrica, Econometric Society, vol. 43(5-6), pages 893-906, Sept.-Nov.
    6. Cosimano, Thomas F., 2008. "Optimal experimentation and the perturbation method in the neighborhood of the augmented linear regulator problem," Journal of Economic Dynamics and Control, Elsevier, vol. 32(6), pages 1857-1894, June.
    7. Tucci, Marco P. & Kendrick, David A. & Amman, Hans M., 2010. "The parameter set in an adaptive control Monte Carlo experiment: Some considerations," Journal of Economic Dynamics and Control, Elsevier, vol. 34(9), pages 1531-1549, September.
    8. Abiodun Egbetokun & Ivan Savin, 2015. "Absorptive Capacity and Innovation: When Is It Better to Cooperate?," Economic Complexity and Evolution, in: Andreas Pyka & John Foster (ed.), The Evolution of Economic and Innovation Systems, edition 127, pages 373-399, Springer.
    9. James G. March, 1991. "Exploration and Exploitation in Organizational Learning," Organization Science, INFORMS, vol. 2(1), pages 71-87, February.
    10. Neck, Reinhard, 1984. "Stochastic control theory and operational research," European Journal of Operational Research, Elsevier, vol. 17(3), pages 283-301, September.
    11. Peter Winker & Marianna Lyra & Chris Sharpe, 2011. "Least median of squares estimation by optimization heuristics with an application to the CAPM and a multi-factor model," Computational Management Science, Springer, vol. 8(1), pages 103-123, April.
    12. D. Blueschke & V. Blueschke-Nikolaeva & R. Neck, 2013. "Stochastic Control of Linear and Nonlinear Econometric Models: Some Computational Aspects," Computational Economics, Springer;Society for Computational Economics, vol. 42(1), pages 107-118, June.
    13. Kendrick, David A., 2005. "Stochastic control for economic models: past, present and the paths ahead," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 3-30, January.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Herrmann, Johannes & Savin, Ivan, 2015. "Evolution of the electricity market in Germany: Identifying policy implications by an agent-based model," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112959, Verein für Socialpolitik / German Economic Association.

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    More about this item

    Keywords

    Differential evolution; stochstic problems; nonlinear optimization; optimal control;
    All these keywords.

    JEL classification:

    • C54 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Quantitative Policy Modeling
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E27 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Forecasting and Simulation: Models and Applications
    • E61 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Policy Objectives; Policy Designs and Consistency; Policy Coordination
    • E63 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Comparative or Joint Analysis of Fiscal and Monetary Policy; Stabilization; Treasury Policy

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