IDEAS home Printed from
   My bibliography  Save this paper

Stochastic Stackelberg equilibria with applications to time dependent newsvendor models


  • 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)


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

    Download full text from publisher

    File URL:
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    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, vol. 2(1), pages 61-68, October.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    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


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

    JEL classification:

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

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hhs:nhhfms:2011_009. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Stein Fossen). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.