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

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  • Moustapha Pemy

Abstract

This paper studies the problem of optimally extracting nonrenewable natural resources. 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, the prices of natural resources are modeled using Markov switching L\'evy processes. We formulate this optimal extraction problem as an infinite-time horizon optimal control problem. We derive closed-form solutions for the value function as well as the optimal extraction policy. Numerical examples are presented to illustrate these results.

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  • Moustapha Pemy, 2018. "Explicit Solutions for Optimal Resource Extraction Problems under Regime Switching L\'evy Models," Papers 1806.06105, arXiv.org.
    • Handle: RePEc:arx:papers:1806.06105
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    References listed on IDEAS

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    1. Harold Hotelling, 1931. "The Economics of Exhaustible Resources," Journal of Political Economy, University of Chicago Press, vol. 39(2), pages 137-137.
    2. Donald A. Hanson, 1980. "Increasing Extraction Costs and Resource Prices: Some Further Results," Bell Journal of Economics, The RAND Corporation, vol. 11(1), pages 335-342, Spring.
    3. Cynthia Lin, C.-Y. & Wagner, Gernot, 2007. "Steady-state growth in a Hotelling model of resource extraction," Journal of Environmental Economics and Management, Elsevier, vol. 54(1), pages 68-83, July.
    4. Rama Cont & Ekaterina Voltchkova, 2005. "A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models," Post-Print halshs-00445645, HAL.
    5. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
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