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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

    as
    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).
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