Martingale Methods for Pricing Inventory Penalties Under Continuous Replenishment and Compound Renewal Demands

Posted: 14 Oct 2015

See all articles by Jim (Junmin) Shi

Jim (Junmin) Shi

New Jersey Institute of Technology

Michael N. Katehakis

Rutgers, The State University of New Jersey - Management Science & Information Systems

Benjamin Melamed

Rutgers, The State University of New Jersey, Rutgers Business School - Newark & New Brunswick, Supply Chain Management Department

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

Suggested Citation

Shi, Jim (Junmin) and Katehakis, Michael N. and Melamed, Benjamin, Martingale Methods for Pricing Inventory Penalties Under Continuous Replenishment and Compound Renewal Demands (October 12, 2013). Annals of Operation Research, Vol. 208, No. 1, 2013, Available at SSRN: https://ssrn.com/abstract=2673328

Jim (Junmin) Shi (Contact Author)

New Jersey Institute of Technology ( email )

University Heights
NJIT
Newark, NJ US 07102
United States
9736427027 (Phone)

HOME PAGE: http://https://web.njit.edu/~jshi/

Michael N. Katehakis

Rutgers, The State University of New Jersey - Management Science & Information Systems ( email )

180 University Ave.
Newark, NJ 07102-1895
United States

Benjamin Melamed

Rutgers, The State University of New Jersey, Rutgers Business School - Newark & New Brunswick, Supply Chain Management Department ( email )

South Tower, Room 3149
100 Rockafeller Rd.
Piscataway, NJ 08854
United States

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