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Simulating Discounted Costs

Author

Listed:
  • Bennett L. Fox

    (Department of Mathematics, University of Colorado, Denver, Colorado 80204-5300)

  • Peter W. Glynn

    (Department of Operations Research, Stanford University, Stanford, California 94305)

Abstract

We numerically estimate, via simulation, the expected infinite-horizon discounted cost d of running a stochastic system. A naive strategy estimates a finite-horizon approximation to d. We propose alternatives. All are ranked with respect to asymptotic variance as a function of computer-time budget and discount rate, when semi-Markov and/or regenerative structure or neither is assumed. In this setting, the naive truncation estimator loses; it may triumph, however, when the computer-time budget is modest, the discount rate is large, and the process simulated is not regenerative or has long cycle lengths.

Suggested Citation

  • Bennett L. Fox & Peter W. Glynn, 1989. "Simulating Discounted Costs," Management Science, INFORMS, vol. 35(11), pages 1297-1315, November.
    • Handle: RePEc:inm:ormnsc:v:35:y:1989:i:11:p:1297-1315
    DOI: 10.1287/mnsc.35.11.1297
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    Cited by:

    1. David B. Brown & James E. Smith, 2013. "Optimal Sequential Exploration: Bandits, Clairvoyants, and Wildcats," Operations Research, INFORMS, vol. 61(3), pages 644-665, June.
    2. Shane G. Henderson & Peter W. Glynn, 2002. "Approximating Martingales for Variance Reduction in Markov Process Simulation," Mathematics of Operations Research, INFORMS, vol. 27(2), pages 253-271, May.
    3. Stephen E. Chick & Noah Gans, 2009. "Economic Analysis of Simulation Selection Problems," Management Science, INFORMS, vol. 55(3), pages 421-437, March.
    4. Cui, Zhenyu & Fu, Michael C. & Peng, Yijie & Zhu, Lingjiong, 2020. "Optimal unbiased estimation for expected cumulative discounted cost," European Journal of Operational Research, Elsevier, vol. 286(2), pages 604-618.
    5. Paul Glasserman & Jeremy Staum, 2003. "Resource Allocation Among Simulation Time Steps," Operations Research, INFORMS, vol. 51(6), pages 908-921, December.

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