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- Title
Optimal production and regulation of gold mining: A stochastic differential game approach.
- Authors
Mutakaya, Masimba Aspinas; Mhlanga, Farai Julius
- Abstract
We treat production and regulation of gold mining on a stock driven by a geometric Brownian motion, and a geometric Lévy process. The mining company seeks to maximise the revenues generated from its extracting activities while the government aims to maximise its share of profits by enacting regulatory policies. The problem is formulated as a non-cooperative stochastic differential game. A verification theorem is presented and proved under the assumption that Fleming-Bellman-Isaacs (FBI) equations have a $ C^{1,2,1} $ solution. We derive closed-forms for the value functions and optimal strategies. The models are calibrated using South African mining data. Numerical results are presented to illustrate the findings of the study as well as the economic interpretation.
- Subjects
DIFFERENTIAL games; LEVY processes; NONRENEWABLE natural resources; BROWNIAN motion; PROFIT-sharing; DATA mining; GOLD mining
- Publication
Journal of Industrial & Management Optimization, 2024, Vol 20, Issue 4, p1
- ISSN
1547-5816
- Publication type
Article
- DOI
10.3934/jimo.2023131