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Total Reward Variance in Discrete and Continuous Time Markov Chains

In: Operations Research Proceedings 2004

Author

Listed:
  • Karel Sladký

    (Academy of Sciences of the Czech Republic)

  • Nico M. Dijk

    (University of Amsterdam)

Abstract

This note studies the variance of total cumulative rewards for Markov reward chains in both discrete and continuous time. It is shown that parallel results can be obtained for both cases. First, explicit formulae are presented for the variance within finite time. Next, the infinite time horizon is considered. Most notably, it is concluded that the variance has a linear growth rate. Explicit expressions are provided, related to the standard average reward case, to compute this growth rate.

Suggested Citation

  • Karel Sladký & Nico M. Dijk, 2005. "Total Reward Variance in Discrete and Continuous Time Markov Chains," Operations Research Proceedings, in: Hein Fleuren & Dick Hertog & Peter Kort (ed.), Operations Research Proceedings 2004, pages 319-326, Springer.
    • Handle: RePEc:spr:oprchp:978-3-540-27679-1_40
    DOI: 10.1007/3-540-27679-3_40
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    Cited by:

    1. Hal Caswell & Fanny Annemarie Kluge, 2015. "Demography and the statistics of lifetime economic transfers under individual stochasticity," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 32(19), pages 563-588.
    2. Bo Li & Antonio Arreola‐Risa, 2021. "On minimizing downside risk in make‐to‐stock, risk‐averse firms," Naval Research Logistics (NRL), John Wiley & Sons, vol. 68(2), pages 199-213, March.

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