The Closed-Form Solution of an Extraction Model and Optimal Stopping Problems with Regime Switching
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....
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| Format: | Article |
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MDPI AG
2023-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/20/4268 |
| _version_ | 1797573071055355904 |
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| author | Yong-Chao Zhang Na Zhang Qinglong Zhou |
| author_facet | Yong-Chao Zhang Na Zhang Qinglong Zhou |
| author_sort | Yong-Chao Zhang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T21:04:27Z |
| format | Article |
| id | doaj.art-1d97258eba574d559626919aa625a48b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T21:04:27Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-1d97258eba574d559626919aa625a48b2023-11-19T17:13:34ZengMDPI AGMathematics2227-73902023-10-011120426810.3390/math11204268The Closed-Form Solution of an Extraction Model and Optimal Stopping Problems with Regime SwitchingYong-Chao Zhang0Na Zhang1Qinglong Zhou2School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Taishan Road 143, Qinhuangdao 066004, ChinaSchool of Mathematical Sciences, Nankai University, Weijin Road 94, Tianjin 300071, ChinaDepartment of Mathematics, Zhejiang University, Yuhangtang Road 866, Hangzhou 310058, ChinaWe 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.https://www.mdpi.com/2227-7390/11/20/4268optimal stoppingregime switchingviscosity solution |
| spellingShingle | Yong-Chao Zhang Na Zhang Qinglong Zhou The Closed-Form Solution of an Extraction Model and Optimal Stopping Problems with Regime Switching Mathematics optimal stopping regime switching viscosity solution |
| title | The Closed-Form Solution of an Extraction Model and Optimal Stopping Problems with Regime Switching |
| title_full | The Closed-Form Solution of an Extraction Model and Optimal Stopping Problems with Regime Switching |
| title_fullStr | The Closed-Form Solution of an Extraction Model and Optimal Stopping Problems with Regime Switching |
| title_full_unstemmed | The Closed-Form Solution of an Extraction Model and Optimal Stopping Problems with Regime Switching |
| title_short | The Closed-Form Solution of an Extraction Model and Optimal Stopping Problems with Regime Switching |
| title_sort | closed form solution of an extraction model and optimal stopping problems with regime switching |
| topic | optimal stopping regime switching viscosity solution |
| url | https://www.mdpi.com/2227-7390/11/20/4268 |
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