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

Junmin Shi (), Michael Katehakis () and Benjamin Melamed ()

Annals of Operations Research, 2013, vol. 208, issue 1, 593-612

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

Keywords: Inventory penalty functions; Martingale; Overage; Risk-neutral pricing; Underage (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (28)

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DOI: 10.1007/s10479-012-1130-5

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