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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.

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File URL: http://hdl.handle.net/11250/164022
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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
Contact details of provider: Postal: NHH, Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway
Phone: +47 55 95 92 93
Fax: +47 55 95 96 50
Web page: http://www.nhh.no/en/research-faculty/department-of-business-and-management-science.aspx
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  1. 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.
  2. T. M. Whitin, 1955. "Inventory Control and Price Theory," Management Science, INFORMS, vol. 2(1), pages 61-68, October.
  3. 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.
  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.
  5. 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.
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