This paper studies the optimal extraction and taxation of nonrenewable natural resources. It is well known  the market values of the main strategic resources such as oil, natural gas, uranium, copper,..., etc, fluctuate randomly following global and seasonal macro-economic parameters, these values are modeled using Markov switching L\'evy processes. 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 differential game as the unique viscosity solutions of the corresponding Hamilton Jacobi Isaacs equations. Furthermore, optimal extraction and taxation policies that should be applied when the equilibrium is reached are derived . In addition, we construct and prove the convergence of a numerical scheme for approximating the value functions and optimal policies. A numerical example is presented to illustrate our findings.
This paper studies the optimal extraction and taxation of nonrenewable natural resources. It is well known that the market values of the main strategic resources such as oil, natural gas, uranium, copper,..., etc, fluctuate randomly following global and seasonal macroeconomic parameters, these values are modeled using Markov switching L\'evy processes. We formulate this problem as a differential game . The two players of this differential game 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 . The corresponding Hamilton Jacobi Isaacs equations are completely solved and the value functions as well as the optimal extraction and taxation rates are derived in closed-form. A Numerical example is presented to illustrate our findings.
A
that
R
macro-economic
macroeconomic
R
where the two players
. The two players of this differential game
R
and characterize
. The corresponding Hamilton Jacobi Isaacs equations are completely solved and
R
of this differential game as the unique viscosity solutions of the corresponding Hamilton Jacobi Isaacs equations. Furthermore,
as well as the
R
policies that should be applied when the equilibrium is reached are derived . In addition, we construct and prove the convergence of a numerical scheme for approximating the value functions and optimal policies. A numerical
rates are derived in closed-form. A Numerical