Optimal forward contract design for inventory: a value-of-waiting analysis

Ostaszewski, Adam ORCID: 0000-0003-2630-8663 and Davies, Roy O. (2019) Optimal forward contract design for inventory: a value-of-waiting analysis. In: Brzdek, Janusz, Popa, Dorian and Rassias, Themistocles M., (eds.) Ulam type stability. Springer International (Firm), Cham, Switzerland, pp. 73-97. ISBN 9783030289713

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Abstract

A classical inventory problem is studied from the perspective of embedded options, reducing inventory-management to the design of optimal contracts for forward delivery of stock (commodity). Financial option techniques à la Black-Scholes are invoked to value the additional ‘option to expand stock’. A simplified approach which ignores distant time effects identifies an optimal ‘time to deliver’ and an optimal ‘amount to deliver’ for a production process run in continuous time modelled by a Cobb-Douglas revenue function. Commodity prices, quoted in initial value terms, are assumed to evolve as a geometric Brownian process with positive (inflationary) drift.Expected revenue maximization identifies an optimal ‘strike price’ for the expansion option to be exercised and reveals the underlying martingale in a truncated (censored) commodity price. The paper establishes comparative statics of the censor, using sensitivity analysis on the related censor functional equation; key here is that the censor, as a function of the drift and volatility of price, is the solution of a functional equation. Asymptotic approximation enables a tractable analysis of the optimal timing

Item Type:	Book Section
Official URL:	https://www.springer.com/gp/book/9783030289713
Additional Information:	© 2019 The Authors
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	05 Jun 2019 13:51
Last Modified:	01 Oct 2024 03:59
URI:	http://eprints.lse.ac.uk/id/eprint/100971

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