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Lost in Translation: Explicitly Solving Nonlinear Stochastic Optimal Control Problems Using the Median Objective Value

Author

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  • Ivan Savin

    () (Karlsruhe Institute of Technology
    UMR 7522 Université de Strasbourg - CNRS
    Friedrich Schiller University of Jena
    Ural Federal University)

  • Dmitri Blueschke

    (Alpen-Adria Universität Klagenfurt)

Abstract

Policy makers constantly face optimal control problems: what controls allow them 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, their restriction to local best solutions only and the symmetry of objective function. The contribution of the current study is that we adopt differential evolution (DE) in the context of nonlinear stochastic optimal control problems, thus ensuring better convergence to a global optimum and explicitly considering parameter uncertainty by evaluating the expected objective function. The latter is done by minimizing the median over a set of multiple Monte Carlo draws of uncertain parameters and by separately evaluating the random parameter draws looking particularly at extreme cases. Comparing DE with more traditional methods, which make use of linear-quadratic optimization, in two economic models, we find that the solutions obtained for expected and ex-post functions differ consistently raising doubts about the optimality of ex-post solutions. We claim that this research is aimed to broaden the range of decision support information used by policy makers when choosing an optimal strategy under much more realistic conditions.

Suggested Citation

  • Ivan Savin & Dmitri Blueschke, 2016. "Lost in Translation: Explicitly Solving Nonlinear Stochastic Optimal Control Problems Using the Median Objective Value," Computational Economics, Springer;Society for Computational Economics, vol. 48(2), pages 317-338, August.
  • Handle: RePEc:kap:compec:v:48:y:2016:i:2:d:10.1007_s10614-015-9526-3
    DOI: 10.1007/s10614-015-9526-3
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    References listed on IDEAS

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    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. Neck, Reinhard, 1984. "Stochastic control theory and operational research," European Journal of Operational Research, Elsevier, vol. 17(3), pages 283-301, September.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Benigno, Pierpaolo & Woodford, Michael, 2012. "Linear-quadratic approximation of optimal policy problems," Journal of Economic Theory, Elsevier, vol. 147(1), pages 1-42.
    9. 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.
    10. Abiodun Egbetokun & Ivan Savin, 2014. "Absorptive capacity and innovation: when is it better to cooperate?," Journal of Evolutionary Economics, Springer, vol. 24(2), pages 399-420, April.
    11. MacRae, Elizabeth Chase, 1975. "An Adaptive Learning Rule for Multiperiod Decision Problems," Econometrica, Econometric Society, vol. 43(5-6), pages 893-906, Sept.-Nov.
    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.
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    Cited by:

    1. Hans M. Amman & Marco Paolo Tucci, 2018. "How active is active learning: value function method vs an approximation method," Department of Economics University of Siena 788, Department of Economics, University of Siena.
    2. Herrmann, J.K. & Savin, I., 2017. "Optimal policy identification: Insights from the German electricity market," Technological Forecasting and Social Change, Elsevier, vol. 122(C), pages 71-90.
    3. D. Blueschke & I. Savin, 2017. "No such thing as a perfect hammer: comparing different objective function specifications for optimal control," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(2), pages 377-392, June.
    4. Hans M. Amman & Marco P. Tucci, 2020. "How Active is Active Learning: Value Function Method Versus an Approximation Method," Computational Economics, Springer;Society for Computational Economics, vol. 56(3), pages 675-693, October.
    5. D. Blueschke & I. Savin & V. Blueschke-Nikolaeva, 2020. "An Evolutionary Approach to Passive Learning in Optimal Control Problems," Computational Economics, Springer;Society for Computational Economics, vol. 56(3), pages 659-673, October.

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