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

In: Ulam Type Stability

Author

Listed:
  • Roy O. Davies

    (University of Leicester, School of Mathematics and Actuarial Science)

  • Adam J. Ostaszewski

    (London School of Economics, Department of Mathematics)

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.

Suggested Citation

  • Roy O. Davies & Adam J. Ostaszewski, 2019. "Optimal Forward Contract Design for Inventory: A Value-of-Waiting Analysis," Springer Books, in: Janusz Brzdęk & Dorian Popa & Themistocles M. Rassias (ed.), Ulam Type Stability, chapter 0, pages 73-96, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-28972-0_4
    DOI: 10.1007/978-3-030-28972-0_4
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