Stochastic Stackelberg equilibria with applications to time dependent newsvendor models
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.
|Date of creation:||19 May 2011|
|Date of revision:|
|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
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- 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.
- T. M. Whitin, 1955. "Inventory Control and Price Theory," Management Science, INFORMS, vol. 2(1), pages 61-68, October.
- 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.
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)
If references are entirely missing, you can add them using this form.