Journal
APPLIED MATHEMATICS AND OPTIMIZATION
Volume 74, Issue 3, Pages 579-618Publisher
SPRINGER
DOI: 10.1007/s00245-016-9390-0
Keywords
Heterogeneous agents model; Mean field games; Master equation; Hamilton Jacobi equations; Viscosity solution; Model calibration
Categories
Funding
- Chaire Finance et developpement durable
- Chaire Economie, finance et gestion des commodites
- ANR [ANR-12-MONU-0013, ANR-16-CE40-0015-01]
Ask authors/readers for more resources
A parcimonious long term model is proposed for a mining industry. Knowing the dynamics of the global reserve, the strategy of each production unit consists of an optimal control problem with two controls, first the flux invested into prospection and the building of new extraction facilities, second the production rate. In turn, the dynamics of the global reserve depends on the individual strategies of the producers, so the models leads to an equilibrium, which is described by low dimensional systems of partial differential equations. The dimensionality depends on the number of technologies that a mining producer can choose. In some cases, the systems may be reduced to a Hamilton-Jacobi equation which is degenerate at the boundary and whose right hand side may blow up at the boundary. A mathematical analysis is supplied. Then numerical simulations for models with one or two technologies are described. In particular, a numerical calibration of the model in order to fit the historical data is carried out.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available