Speaker: Yves Achdou (LJLL, Université Paris-Diderot)

Titre: A short-term model for the oil industry addressing commercial storage

A joint work with C.Bertucci (CNRS), J.-M. Lasry (U. Dauphine), P.-L. Lions (Collège de France), A. Rostand (Kayrros), J. Scheinkman (Columbia U.)

Résumé:
We propose a mechanism for the short term dynamics of the oil market based on the interactions of several agents,
namely a major agent (a monopolistic cartel), a fringe of competitive producers and a crowd of physical arbitrageurs who store the resource. The model leads to a system of two coupled non linear partial differential equations, with a new type of boundary conditions linked to constraints on the storage capacity.
These boundary conditions play a key role and translate the fact that when storage is either full or empty, the cartel has an enhanced strategic power, and may tune the price of the resource.
The model will be discussed in details. Numerical simulations based on a finite difference scheme will be reported. The latter result in apparently surprising
facts:
1) the optimal control of the cartel (i.e. its level of production) is a discontinuous function of the state variables;
2) there is a cycle, which takes place around the shock line.
These phenomena will be discussed, and it will be shown that they may explain what happened in 2015 and 2020.

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