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A stochastic optimal stopping model for storable commodity prices

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  • Karimi, Nader
  • Salavati, Erfan
  • Assa, Hirbod
  • Adibi, Hojatollah

Abstract

In this paper, we propose a continuous time version of the well-known speculative storage model for commodity prices. But from the mathematical point of view this is not a trivial extension and needs careful consideration of the theory of stochastic stopping time combined with fixed point theory. We formulate the problem in a manner that the main objective of the storage model, known as the stationary rational expectations equilibrium (SREE), becomes a fixed-point of an operator which solves a free boundary problem and show that this operator under some conditions is a contraction. We also demonstrate the benefits of our continuous time model through a numerical algorithm.

Suggested Citation

  • Karimi, Nader & Salavati, Erfan & Assa, Hirbod & Adibi, Hojatollah, 2024. "A stochastic optimal stopping model for storable commodity prices," Statistics & Probability Letters, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:stapro:v:204:y:2024:i:c:s0167715223001657
    DOI: 10.1016/j.spl.2023.109941
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    References listed on IDEAS

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    1. Angus Deaton & Guy Laroque, 1992. "On the Behaviour of Commodity Prices," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(1), pages 1-23.
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    5. Casassus, Jaime & Collin-Dufresne, Pierre & Routledge, Bryan R., 2018. "Equilibrium commodity prices with irreversible investment and non-linear technologies," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 128-147.
    6. Deaton, Angus & Laroque, Guy, 1996. "Competitive Storage and Commodity Price Dynamics," Journal of Political Economy, University of Chicago Press, vol. 104(5), pages 896-923, October.
    7. David M Arseneau & Sylvain Leduc, 2013. "Commodity Price Movements in a General Equilibrium Model of Storage," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 61(1), pages 199-224, April.
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    10. Deaton, Angus & Laroque, Guy, 1995. "Estimating a Nonlinear Rational Expectations Commodity Price Model with Unobservable State Variables," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(S), pages 9-40, Suppl. De.
    11. Cafiero, Carlo & Bobenrieth H., Eugenio S.A. & Bobenrieth H., Juan R.A. & Wright, Brian D., 2011. "The empirical relevance of the competitive storage model," Journal of Econometrics, Elsevier, vol. 162(1), pages 44-54, May.
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    13. Steven D. Baker, 2021. "The Financialization of Storable Commodities," Management Science, INFORMS, vol. 67(1), pages 471-499, January.
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