  This paper studies the optimal extraction policy of an oil field as well as
the efficient taxation of the revenues generated. 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. Given 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 the
convergence of an approximating scheme for the value functions. 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.
