Bernt Øksendal
University of Oslo
Optimal pricing strategies and Stackelberg equilibria in time
delayed stochastic differential games.
Abstract:
In the classical newsvendor problem there are two agents:
(i) The manufacturer, who today (i.e. at time t\delta) decides the
unit price to sell the manufactured goods for to the retailer, with
delivery tomorrow (at time t)
(ii) The retailer, who then today (at time t\delta) decides the
quantity to order from the manufacturer and the price to sell each
item for to the public the next day.
What is the optimal price set by the manufacturer and the optimal
quantity to order and the optimal retailer price? The problem is that
neither of these agents know what the demand will be the next day,
only its probabilistic distribution. This is a problem that occurs in
many situations, for example in the pricing of electricity in a
liberated electricity market.
We generalize this classical newsvendor problem to continuous time and
a jump diffusion setting, and formulate it as a problem to find the
Stackelberg equilibrium of a stochastic differential game with delayed
information flow. We find a maximum principle for this type of control
problem, and use it to solve the optimal pricing problem in some
specific cases.
The presentation is based on recent joint work with Leif Sandal and
Jan Ubøe, both at NHH, Bergen, Norway.
