Martingale Methods for Pricing Inventory Penalties Under Continuous Replenishment and Compound Renewal Demands
Posted: 14 Oct 2015
Date Written: October 12, 2013
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
Keywords: Inventory penalty functions, Martingale, Overage, Risk-neutral pricing, Underage
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