Stochastic Stackelberg Equilibria with Applications to Time Dependent Newsvendor Models

38 Pages Posted: 28 May 2011

See all articles by Bernt Oksendal

Bernt Oksendal

University of Oslo - Department of Mathematics

Leif Kristoffer Sandal

Norwegian School of Economics (NHH) - Department of Business and Management Science

Jan Uboe

Norwegian School of Economics (NHH) - Department of Business and Management Science

Date Written: May 19, 2011

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

Suggested Citation

Oksendal, Bernt and Sandal, Leif Kristoffer and Uboe, Jan, Stochastic Stackelberg Equilibria with Applications to Time Dependent Newsvendor Models (May 19, 2011). NHH Dept. of Finance & Management Science Discussion Paper No. 2011/9. Available at SSRN: https://ssrn.com/abstract=1846479 or http://dx.doi.org/10.2139/ssrn.1846479

Bernt Oksendal

University of Oslo - Department of Mathematics ( email )

P.O. Box 1053
Blindern, N-0162, Os
Norway
+47-2285 5913 (Phone)
+47-2285 4349 (Fax)

Leif Kristoffer Sandal

Norwegian School of Economics (NHH) - Department of Business and Management Science ( email )

Helleveien 30
Bergen, NO-5045
Norway
+47 55 95 93 41 (Phone)

Jan Uboe (Contact Author)

Norwegian School of Economics (NHH) - Department of Business and Management Science ( email )

Helleveien 30
Bergen, NO-5045
Norway

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