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The Closed-Form Solution of an Extraction Model and Optimal Stopping Problems with Regime Switching

Author

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  • Yong-Chao Zhang

    (School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Taishan Road 143, Qinhuangdao 066004, China)

  • Na Zhang

    (School of Mathematical Sciences, Nankai University, Weijin Road 94, Tianjin 300071, China)

  • Qinglong Zhou

    (Department of Mathematics, Zhejiang University, Yuhangtang Road 866, Hangzhou 310058, China)

Abstract

We aim to obtain by viscosity solution method the closed-form solution of a model concerning natural resource extraction in which a firm draws a schedule of when to stop the extraction. In this model, a regime-switching stochastic process is introduced to simulate the price of some natural resource. To solve the model, we first develop a theory, as a part of the results in the paper, that also applies to other optimal stopping problems containing regime-switching ingredients. Then using the theory, we solve the model completely and rigorously. A numerical example is given to display the results of the model.

Suggested Citation

  • Yong-Chao Zhang & Na Zhang & Qinglong Zhou, 2023. "The Closed-Form Solution of an Extraction Model and Optimal Stopping Problems with Regime Switching," Mathematics, MDPI, vol. 11(20), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4268-:d:1258761
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    References listed on IDEAS

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    1. Ferrari, Giorgio & Koch, Torben, 2018. "An optimal extraction problem with price impact," Center for Mathematical Economics Working Papers 603, Center for Mathematical Economics, Bielefeld University.
    2. Ma, Qiang & Liu, Xin & Wang, Wei-Guo & Xue, Jing, 2023. "Natural resources extraction and COP26 target: Evaluating the role of green finance," Resources Policy, Elsevier, vol. 82(C).
    3. Dixit, Avinash K, 1989. "Entry and Exit Decisions under Uncertainty," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 620-638, June.
    4. Tsekrekos, Andrianos E., 2010. "The effect of mean reversion on entry and exit decisions under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 725-742, April.
    5. Giorgio Ferrari & Torben Koch, 2018. "An Optimal Extraction Problem with Price Impact," Papers 1812.01270, arXiv.org.
    6. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    7. Bae, Geum Il & Kim, Woo Chang & Mulvey, John M., 2014. "Dynamic asset allocation for varied financial markets under regime switching framework," European Journal of Operational Research, Elsevier, vol. 234(2), pages 450-458.
    8. Casassus, Jaime & Collin-Dufresne, Pierre & Routledge, Bryan R., 2018. "Equilibrium commodity prices with irreversible investment and non-linear technologies," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 128-147.
    9. Ramin Dadasov & Carsten Hefeker & Oliver Lorz, 2017. "Natural resource extraction, corruption, and expropriation," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 153(4), pages 809-832, November.
    10. Teng, Yin-Pei, 2023. "Natural resources extraction and sustainable development: Linear and non-linear resources curse hypothesis perspective for high income countries," Resources Policy, Elsevier, vol. 83(C).
    11. Liu, Lili, 2023. "Natural resources extraction and global COP26 target: An overview of USA economy," Resources Policy, Elsevier, vol. 82(C).
    12. Janus, Thorsten, 2012. "Natural resource extraction and civil conflict," Journal of Development Economics, Elsevier, vol. 97(1), pages 24-31.
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