  This paper studies the problem of optimally extracting nonrenewable natural
resource in light of various financial and economic restrictions and
constraints. Taking into account the fact that the market values of the main
natural resources i.e. oil, natural gas, 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
finite-time horizon combined optimal stopping and optimal control problem. We
prove that the value function is the unique viscosity solution of the
corresponding Hamilton-Jacobi-Bellman equations. Moreover, we prove the
convergence of a finite difference approximation of the value function.
Numerical examples are presented to illustrate these results.
