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Stochastic Stackelberg equilibria with applications to time dependent newsvendor models

Author

Listed:
  • Øksendal, Bernt

    () (Dept. of Mathematics, University of Oslo)

  • Sandal, Leif K.

    () (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

  • Ubøe, Jan

    () (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

Abstract

In this paper we prove a sufficient maximum principle for general stochastic differential Stackelberg games, and apply the theory to continuous time newsvendor problems. In the newsvendor problem a manufacturer sells goods to a retailer, and the objective of both parties is to maximize expected profits under a random demand rate. Our demand rate is an Ito-Levy process, and to increase realism information is delayed, e.g., due to production time. We provide complete existence and uniqueness proofs for a series of special cases, including geometric Brownian motion and the Ornstein-Uhlenbeck process, both with time variable coefficients. Moreover, these results are operational because we are able to offer explicit solution formulas. An interesting finding is that more precise information may be a considerable disadvantage for the retailer.

Suggested Citation

  • Øksendal, Bernt & Sandal, Leif K. & Ubøe, Jan, 2011. "Stochastic Stackelberg equilibria with applications to time dependent newsvendor models," Discussion Papers 2011/9, Norwegian School of Economics, Department of Business and Management Science.
  • Handle: RePEc:hhs:nhhfms:2011_009
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    File URL: http://hdl.handle.net/11250/164022
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    References listed on IDEAS

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    1. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71.
    2. Yong, Jiongmin, 2006. "Backward stochastic Volterra integral equations and some related problems," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 779-795, May.
    3. Wang, Haifeng & Chen, Bocheng & Yan, Houmin, 2010. "Optimal inventory decisions in a multiperiod newsvendor problem with partially observed Markovian supply capacities," European Journal of Operational Research, Elsevier, vol. 202(2), pages 502-517, April.
    4. Kogan, Konstantin & Lou, Sheldon, 2003. "Multi-stage newsboy problem: A dynamic model," European Journal of Operational Research, Elsevier, vol. 149(2), pages 448-458, September.
    5. T. M. Whitin, 1955. "Inventory Control and Price Theory," Management Science, INFORMS, pages 61-68.
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    Cited by:

    1. repec:wsi:apjorx:v:34:y:2017:i:06:n:s0217595917500312 is not listed on IDEAS
    2. Sandal, Leif K. & Ubøe, Jan, 2012. "Stackelberg equilibria in a multiperiod vertical contracting model with uncertain and price-dependent demand," Discussion Papers 2012/2, Norwegian School of Economics, Department of Business and Management Science.
    3. Youkyung Won, 2016. "Dominance Relationship Among the Retailer’s Strategies Under the Semi-Stackelberg Newsvendor Situation with Quantity Discounts," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(02), pages 1-20, April.
    4. Beißner, Patrick & Lin, Qian & Riedel, Frank, 2016. "Dynamically consistent α-Maxmin expected utility," Center for Mathematical Economics Working Papers 535, Center for Mathematical Economics, Bielefeld University.
    5. Azad Gholami, Reza & Sandal, Leif K. & Ubøe, Jan, 2016. "Channel Coordination in a Multi-period Newsvendor Model with Dynamic, Price-dependent Stochastic Demand," Discussion Papers 2016/6, Norwegian School of Economics, Department of Business and Management Science.

    More about this item

    Keywords

    Stochastic differential games; newsvendor model; delayed information; Ito-Levy processes;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General

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