The First Passage Time Problem for Mixed-Exponential Jump Processes with Applications in Insurance and Finance
This paper studies the first passage times to constant boundaries for mixed-exponential jump diffusion processes. Explicit solutions of the Laplace transforms of the distribution of the first passage times, the joint distribution of the first passage times and undershoot (overshoot) are obtained. As...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/571724 |
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| _version_ | 1832550644487028736 |
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| author | Chuancun Yin Yuzhen Wen Zhaojun Zong Ying Shen |
| author_facet | Chuancun Yin Yuzhen Wen Zhaojun Zong Ying Shen |
| author_sort | Chuancun Yin |
| collection | DOAJ |
| description | This paper studies the first passage times to constant boundaries for mixed-exponential jump diffusion processes. Explicit solutions of the Laplace transforms of the distribution of the first passage times, the joint distribution of the first passage times and undershoot (overshoot) are obtained. As applications, we present explicit expression of the Gerber-Shiu functions for surplus processes with two-sided jumps, present the analytical solutions for popular path-dependent options such as lookback and barrier options in terms of Laplace transforms, and give a closed-form expression on the price of the zero-coupon bond under a structural credit risk model with jumps. |
| format | Article |
| id | doaj-art-9b6db8390ac34b889fe40104592328f3 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-9b6db8390ac34b889fe40104592328f32025-02-03T06:06:18ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/571724571724The First Passage Time Problem for Mixed-Exponential Jump Processes with Applications in Insurance and FinanceChuancun Yin0Yuzhen Wen1Zhaojun Zong2Ying Shen3School of Mathematical Sciences, Qufu Normal University, Shandong 273165, ChinaSchool of Mathematical Sciences, Qufu Normal University, Shandong 273165, ChinaSchool of Mathematical Sciences, Qufu Normal University, Shandong 273165, ChinaSchool of Mathematical Sciences, Qufu Normal University, Shandong 273165, ChinaThis paper studies the first passage times to constant boundaries for mixed-exponential jump diffusion processes. Explicit solutions of the Laplace transforms of the distribution of the first passage times, the joint distribution of the first passage times and undershoot (overshoot) are obtained. As applications, we present explicit expression of the Gerber-Shiu functions for surplus processes with two-sided jumps, present the analytical solutions for popular path-dependent options such as lookback and barrier options in terms of Laplace transforms, and give a closed-form expression on the price of the zero-coupon bond under a structural credit risk model with jumps.http://dx.doi.org/10.1155/2014/571724 |
| spellingShingle | Chuancun Yin Yuzhen Wen Zhaojun Zong Ying Shen The First Passage Time Problem for Mixed-Exponential Jump Processes with Applications in Insurance and Finance Abstract and Applied Analysis |
| title | The First Passage Time Problem for Mixed-Exponential Jump Processes with Applications in Insurance and Finance |
| title_full | The First Passage Time Problem for Mixed-Exponential Jump Processes with Applications in Insurance and Finance |
| title_fullStr | The First Passage Time Problem for Mixed-Exponential Jump Processes with Applications in Insurance and Finance |
| title_full_unstemmed | The First Passage Time Problem for Mixed-Exponential Jump Processes with Applications in Insurance and Finance |
| title_short | The First Passage Time Problem for Mixed-Exponential Jump Processes with Applications in Insurance and Finance |
| title_sort | first passage time problem for mixed exponential jump processes with applications in insurance and finance |
| url | http://dx.doi.org/10.1155/2014/571724 |
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