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Martingale methods for pricing inventory penalties under continuous replenishment and compound renewal demands

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  • Junmin Shi
  • Michael Katehakis
  • Benjamin Melamed

Abstract

This paper addresses the problem of inventory penalty pricing under the risk-neutral valuation principle. The underlying production-inventory system has a constant replenishment rate and a compound renewal demand stream (i.e., iid demand interarrival times are independent of iid demand sizes), and is subject to underage and overage penalties. Our pricing approach treats the penalties as a series of perpetual American options, and constructs auxiliary martingale processes in term of the inventory process. We provide a necessary and sufficient martingale condition for general compound renewal demands. Explicit expressions of penalty functions for underage and overage are obtained for the case where demand arrivals follow a Poisson process. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Junmin Shi & Michael Katehakis & Benjamin Melamed, 2013. "Martingale methods for pricing inventory penalties under continuous replenishment and compound renewal demands," Annals of Operations Research, Springer, vol. 208(1), pages 593-612, September.
    • Handle: RePEc:spr:annopr:v:208:y:2013:i:1:p:593-612:10.1007/s10479-012-1130-5
    DOI: 10.1007/s10479-012-1130-5
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    References listed on IDEAS

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