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Stochastic Stackelberg equilibria with applications to time dependent newsvendor models

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Author Info

  • 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.

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Bibliographic Info

Paper provided by Department of Business and Management Science, Norwegian School of Economics in its series Discussion Papers with number 2011/9.

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Length: 37 pages
Date of creation: 19 May 2011
Date of revision:
Handle: RePEc:hhs:nhhfms:2011_009

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Web page: http://www.nhh.no/en/research-faculty/department-of-business-and-management-science.aspx
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Related research

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

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  1. 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.
  2. T. M. Whitin, 1955. "Inventory Control and Price Theory," Management Science, INFORMS, vol. 2(1), pages 61-68, October.
  3. 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.
  4. 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.
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Cited by:
  1. Sandal, Leif K. & Ubøe, Jan, 2012. "Stackelberg equilibria in a multiperiod vertical contracting model with uncertain and price-dependent demand," Discussion Papers 2012/2, Department of Business and Management Science, Norwegian School of Economics.

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