Title: Optimal Oil Production and Taxation under Carbon Emission Constraints.
Abstract: We study the optimal extraction policy of an oil field as well as the efficient taxation of the revenues generated in light of various economic restrictions and constraints. Taking into account the fact that the oil price in worldwide commodity markets fluctuates randomly following global and seasonal macroeconomic parameters, we model the evolution of the oil price as a mean reverting regime-switching jump diffusion process. Moreover, taking into account the fact that oil producing countries rely on oil sale revenues as well as taxes levied on oil companies for a good portion of the revenue side of their budgets, we formulate this problem as a differential game where the two players are the mining company whose aim is to maximize the revenues generated from its extracting activities and the government agency in charge of regulating and taxing natural resources. We prove the existence of a Nash equilibrium and characterize the value functions of this stochastic differential game as the unique viscosity solutions of the corresponding Hamilton Jacobi Isaacs equations. Furthermore, optimal extraction and fiscal policies that should be applied when the equilibrium is reached are derived. A numerical example is presented to illustrate these results.