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Optimal Option Purchasing Decisions for the Risk-Averse Retailer with Shortage Cost

Author

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  • Xin-Sheng Xu

    (College of Science, Binzhou University, Binzhou 256600, P. R. China)

  • Felix T. S. Chan

    (Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Kowloon 999077, Hong Kong)

Abstract

To hedge against potential risks, this paper introduces the conditional value-at-risk (CVaR) measure into the option purchasing for the risk-averse retailer with shortage cost. We introduce two models for the risk-averse retailer to select the optimal option purchase quantity. It is found that both two optimal option purchase quantities to two models can be decreasing in the retail price and increasing in the option executing price under certain conditions. This is different from the optimal option purchase quantity for a risk-neutral retailer to maximize the expected profit. It is found that both two optimal option purchase quantities may be increasing or decreasing in the confidence level, which implies a retailer who becomes more risk-averse may purchase more or fewer options to hedge against potential risks. Under both two optimal option purchase quantities, it is proven that the retailer’s expected profit is decreasing in the confidence level. This confirms the fact that high return implies high risk while low risk comes with low return.

Suggested Citation

  • Xin-Sheng Xu & Felix T. S. Chan, 2019. "Optimal Option Purchasing Decisions for the Risk-Averse Retailer with Shortage Cost," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(02), pages 1-25, April.
    • Handle: RePEc:wsi:apjorx:v:36:y:2019:i:02:n:s0217595919400050
    DOI: 10.1142/S0217595919400050
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    References listed on IDEAS

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    Cited by:

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    3. Xing, Wei & Li, Qiankun & Zhao, Xuan & Li, Jialu, 2020. "Information sale and contract selection under downstream competition," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 136(C).
    4. Xiaoqing Liu & Gongli Luo & Xinsheng Xu, 2022. "Optimal Purchasing Decisions with Supplier Default in Portfolio Procurement," Mathematics, MDPI, vol. 10(17), pages 1-10, September.

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