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

Yong-Chao Zhang (), Na Zhang and Qinglong Zhou ()
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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

Mathematics, 2023, vol. 11, issue 20, 1-16

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.

Keywords: optimal stopping; regime switching; viscosity solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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