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This paper studies the problem of optimally extracting nonrenewable naturalresources. Taking into account the fact that the market values of the mainnatural resources i.e. oil, natural gas, copper,..., etc, fluctuate randomlyfollowing global and seasonal macroeconomic parameters, the prices of naturalresources are modeled using Markov switching L\'evy processes. We formulatethis optimal extraction problem as an infinite-time horizon optimal controlproblem. We derive closed-form solutions for the value function as well as theoptimal extraction policy. Numerical examples are presented to illustrate theseresults.

Explicit Solutions for Optimal Resource Extraction Problems under Regime Switching L\'evy Models