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A market-based martingale valuation approach to optimum inventory control in a doubly stochastic jump-diffusion economy

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  • Jack SK Chang

    (Department of Finance and Law, California State University, Los Angeles, USA)

  • Carolyn Chang

    (Department of Finance, California State University, Fullerton, USA)

  • Min Shi

    (Department of Management, California State University, Los Angeles, USA)

Abstract

We propose a novel market-based approach to optimum inventory control in a doubly stochastic jump-diffusion economy by modelling a commodity distributor’s inventory investment as a portfolio of forward commitments with explicit accounting of the jump-diffusion dynamics of demands, costs, and prices in open markets. We apply the robust real-asset martingale valuation methodology to derive a closed-form solution for the inventory value and a simple and intuitive optimality condition. Numerical analysis verifies this condition and demonstrates that the resulting optimum policy has robust properties in relation to the stylized effects.

Suggested Citation

  • Jack SK Chang & Carolyn Chang & Min Shi, 2015. "A market-based martingale valuation approach to optimum inventory control in a doubly stochastic jump-diffusion economy," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(3), pages 405-420, March.
    • Handle: RePEc:pal:jorsoc:v:66:y:2015:i:3:p:405-420
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    Cited by:

    1. Yufeng Zhuang & Ningxi Zhang & Song Wang & Yanzhu Hu, 2019. "Optimal Logistics Control of an Omnichannel Supply Chain," Sustainability, MDPI, vol. 11(21), pages 1-16, October.
    2. William W. Wilson & Jesse Klebe, 2021. "Commodity procurement as contingent claims: Capturing risk and real options in flour milling," Agribusiness, John Wiley & Sons, Ltd., vol. 37(2), pages 348-370, April.

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