A class of short-term models for the oil industry that accounts for speculative oil storage

by Yves Achdou1, Charles Bertucci2, Jean-Michel Lasry 3, Pierre-Louis Lions4, Antoine Rostand5 and José A. Scheinkman6
1Université de Paris Cité and Sorbonne Université, CNRS, Laboratoire Jacques-Louis Lions, (LJLL), F-75006 Paris, France
(email: achdou@ljll-univ-paris-diderot.fr)
2École polytechnique, France
(email: charles.bertucci@polytechnique.edu)
3Université Paris-Dauphine, France
(email: ---)
4Collège de France, Paris, France
(email: ---)
5Kayrros Paris, France
(email: a.rostand@kayrros.com)
6Columbia University, New-York, USA and Princeton University and NBER
(email: js3317@columbia.edu)


We propose a plausible mechanism for the short term dynamics of the oil market based on the interaction of a cartel, a fringe of competitive producers, and a crowd of capacity-constrained physical arbitrageurs that store the resource. The model leads to a system of two coupled nonlinear partial differential equations, with a new type of boundary conditions that play a key role and translate the fact that when storage is either full or empty, the cartel has enhanced strategic power. We propose a finite difference scheme and report numerical simulations. Simulations show apparently surprising patterns: the optimal control of the cartel, the level of a line of discontinuity. These patterns help explain remarkable price swings in oil prices in 2015 and 2020.

Key words:

Economics of oil industry, Major agent facing a crowd of physical arbitrageurs, Boundary conditions linked to state constraints
JEL Classification:  C61, C73, D43, L13, Q02, Q41
Mathematics Subject Classification (2020):  49N80, 91A16, 91B69, 91B52