Pricing Overage and Underage Penalties for Inventory with Continuous Replenishment and Compound Renewal Demand via Martingale Methods
نویسندگان
چکیده
This paper addresses the inventory penalty pricing problem under risk-neutral valuation principle. In particular, we consider an inventory driven by a constant replenishment rate and compound renewal demand stream (iid demand inter-arrival time and iid demand quantity), and subject to overage penalties and underage penalties. Our solution approach treats the inventory penalties of overage and underage as a series of American options and constructs auxiliary martingale processes in term of inventory process. We provide a necessary and sufficient martingale condition for general compound renewal demands. For the case with compound Poisson demands, explicit expressions of penalty functions for the underage and overage are obained.
منابع مشابه
Martingale methods for pricing inventory penalties under continuous replenishment and compound renewal demands
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 serie...
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