EPRasheed wishes to be able to model and predict oil prices out to a time-horizon of 2050, taking into account a number of known factors. These include the finite supply of oil, growing and shifting demand, the viability of alternative energy sources (at different pricing levels) and the interactions of oil producers and oil consumers, as they respond to current pricing levels.

The study group concluded that while ‘prediction’ of price in any meaningful sense was not viable, a model for scenario analysis could be realised. The model did not incorporate all of the factors of interest, but did model important time lags in the response of market players’ future behaviour to current oil prices.

Consideration of the optimisation of supply through new capacity in the telecoms industry led to a generalisation of the standard Cournot-Nash equilibrium. This indicates how an output-constrained competitive market might operate. It enables identification of different pricing regimes determined by the level of competition and the resource limitations of particular supplier firms.

Two models were developed sufficiently to enable simulation of various conditions and events. The first modelled oil price as a mean reverting Brownian motion process. Strategies and scenarios were included in the model and realistic simulations were produced. The second approach used stability analysis of an appropriate time-delayed differential equation. This enabled the identification of unstable conditions and the realisation of price oscillations which depended on the demand scenarios.

Problem presented by
Wajid Rasheed, EPRasheed

Study Group contributors
Chris Dent (University of Edinburgh)
Kamil Kulesza (Systems Research Institute PAS)
Robert Leese (Industrial Mathematics KTN)
Nick McCullen (University of Bath)
Magda Muter (Warsaw School of Economics)
Karina Piwarska (University of Warsaw)
Colin Please (University of Southampton)
Pawel Szerling (University of Warsaw)
Eddie Wilson (University of Bristol)
Yichao Zhu (OCIAM, University of Oxford)