Mathematical Finance Seminar
HUB, RUD 25; 1.115
Yves Achdou (Universite de Paris)

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

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. 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) the optimal trajectories (in the state variables) are cycles which take place around the discontinuity line. These patterns help explain remarkable price swings in oil prices in 2015 and 2020.

The talk is based on joint work with C. Bertucci, J.M Lasry, P.L Lions, A. Rostand and J. Scheinkman.