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Department of Business and Management Science, Norwegian School of Economics (NHH) Discussion Papers, Department of Business and Management Science, Norwegian School of Economics (NHH)

No 2011/9:
Stochastic Stackelberg equilibria with applications to time dependent newsvendor models

Bernt Øksendal (), Leif K. Sandal () and Jan Ubøe ()

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.

Keywords: Stochastic differential games; newsvendor model; delayed information; Ito-Levy processes; (follow links to similar papers)

JEL-Codes: C00; (follow links to similar papers)

37 pages, May 19, 2011

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