Optimal Forward Contract Design for Inventory: A Value-of-Waiting Analysis

Roy O. Davies and Adam J. Ostaszewski ()
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Roy O. Davies: University of Leicester, School of Mathematics and Actuarial Science
Adam J. Ostaszewski: London School of Economics, Department of Mathematics

Chapter Chapter 4 in Ulam Type Stability, 2019, pp 73-96 from Springer

Abstract: 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 allows a tractable analysis of the optimal timing.

Keywords: Value of waiting; Censor functional equation; Optimal forward contract; Optimal exercise price; Optimal timing; Comparative statics; Asymptotic approximation; Martingale; Primary 91B32, 91B38, 39B22; Secondary 91G80, 49J55, 49K40 (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-28972-0_4

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DOI: 10.1007/978-3-030-28972-0_4

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