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EM Algorithm and Stochastic Control in Economics

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  • Steven Kou
  • Xianhua Peng
  • Xingbo Xu

Abstract

Generalising the idea of the classical EM algorithm that is widely used for computing maximum likelihood estimates, we propose an EM-Control (EM-C) algorithm for solving multi-period finite time horizon stochastic control problems. The new algorithm sequentially updates the control policies in each time period using Monte Carlo simulation in a forward-backward manner; in other words, the algorithm goes forward in simulation and backward in optimization in each iteration. Similar to the EM algorithm, the EM-C algorithm has the monotonicity of performance improvement in each iteration, leading to good convergence properties. We demonstrate the effectiveness of the algorithm by solving stochastic control problems in the monopoly pricing of perishable assets and in the study of real business cycle.

Suggested Citation

  • Steven Kou & Xianhua Peng & Xingbo Xu, 2016. "EM Algorithm and Stochastic Control in Economics," Papers 1611.01767, arXiv.org.
    • Handle: RePEc:arx:papers:1611.01767
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    References listed on IDEAS

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    1. Christiano, Lawrence J, 1990. "Linear-Quadratic Approximation and Value-Function Iteration: A Comparison," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 99-113, January.
    2. David B. Brown & James E. Smith, 2014. "Information Relaxations, Duality, and Convex Stochastic Dynamic Programs," Operations Research, INFORMS, vol. 62(6), pages 1394-1415, December.
    3. Guillermo Gallego & Garrett van Ryzin, 1994. "Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons," Management Science, INFORMS, vol. 40(8), pages 999-1020, August.
    4. Idris Kharroubi & Nicolas Langren'e & Huy^en Pham, 2013. "A numerical algorithm for fully nonlinear HJB equations: an approach by control randomization," Papers 1311.4503, arXiv.org.
    5. repec:dau:papers:123456789/5524 is not listed on IDEAS
    6. David B. Brown & James E. Smith & Peng Sun, 2010. "Information Relaxations and Duality in Stochastic Dynamic Programs," Operations Research, INFORMS, vol. 58(4-part-1), pages 785-801, August.
    7. repec:dau:papers:123456789/5522 is not listed on IDEAS
    8. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    9. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    10. Hansen, Gary D., 1985. "Indivisible labor and the business cycle," Journal of Monetary Economics, Elsevier, vol. 16(3), pages 309-327, November.
    11. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
    12. Guillermo Gallego & Garrett van Ryzin, 1997. "A Multiproduct Dynamic Pricing Problem and Its Applications to Network Yield Management," Operations Research, INFORMS, vol. 45(1), pages 24-41, February.
    13. Bouchard, Bruno & Touzi, Nizar, 2004. "Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 175-206, June.
    14. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    15. Long, John B, Jr & Plosser, Charles I, 1983. "Real Business Cycles," Journal of Political Economy, University of Chicago Press, vol. 91(1), pages 39-69, February.
    16. Idris Kharroubi & Nicolas Langrené & Huyên Pham, 2013. "A numerical algorithm for fully nonlinear HJB equations: an approach by control randomization," Working Papers hal-00905899, HAL.
    17. Lars Peter Hansen & Thomas J. Sargent, 2013. "Recursive Models of Dynamic Linear Economies," Economics Books, Princeton University Press, edition 1, number 10141.
    18. Mark Broadie & Deniz Cicek & Assaf Zeevi, 2011. "General Bounds and Finite-Time Improvement for the Kiefer-Wolfowitz Stochastic Approximation Algorithm," Operations Research, INFORMS, vol. 59(5), pages 1211-1224, October.
    19. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
    20. Crisan, D. & Manolarakis, K. & Touzi, N., 2010. "On the Monte Carlo simulation of BSDEs: An improvement on the Malliavin weights," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1133-1158, July.
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