The Exit Time and the Dividend Value Function for One-Dimensional Diffusion Processes
We investigate the exit times from an interval for a general one-dimensional time-homogeneous diffusion process and their applications to the dividend problem in risk theory. Specifically, we first use Dynkin’s formula to derive the ordinary differential equations satisfied by the Laplace transform...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/675202 |
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| _version_ | 1832560606948884480 |
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| author | Peng Li Chuancun Yin Ming Zhou |
| author_facet | Peng Li Chuancun Yin Ming Zhou |
| author_sort | Peng Li |
| collection | DOAJ |
| description | We investigate the exit times from an interval for a general one-dimensional time-homogeneous diffusion process and their applications to the dividend problem in risk theory. Specifically, we first use Dynkin’s formula to derive the ordinary differential equations satisfied by the Laplace transform of the exit times. Then, as some examples, we solve the closed-form expression of the Laplace transform of the exit times for several popular diffusions, which are commonly used in modelling of finance and insurance market. Most interestingly, as the applications of the exit times, we create the connect between the dividend value function and the Laplace transform of the exit times. Both the barrier and threshold dividend value function are clearly expressed in terms of the Laplace transform of the exit times. |
| format | Article |
| id | doaj-art-8b95b6756d2d4f2eaf737b40c6c9bd2e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8b95b6756d2d4f2eaf737b40c6c9bd2e2025-02-03T01:27:14ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/675202675202The Exit Time and the Dividend Value Function for One-Dimensional Diffusion ProcessesPeng Li0Chuancun Yin1Ming Zhou2School of Mathematical Sciences, Qufu Normal University, Shandong 273165, ChinaSchool of Mathematical Sciences, Qufu Normal University, Shandong 273165, ChinaChina Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, ChinaWe investigate the exit times from an interval for a general one-dimensional time-homogeneous diffusion process and their applications to the dividend problem in risk theory. Specifically, we first use Dynkin’s formula to derive the ordinary differential equations satisfied by the Laplace transform of the exit times. Then, as some examples, we solve the closed-form expression of the Laplace transform of the exit times for several popular diffusions, which are commonly used in modelling of finance and insurance market. Most interestingly, as the applications of the exit times, we create the connect between the dividend value function and the Laplace transform of the exit times. Both the barrier and threshold dividend value function are clearly expressed in terms of the Laplace transform of the exit times.http://dx.doi.org/10.1155/2013/675202 |
| spellingShingle | Peng Li Chuancun Yin Ming Zhou The Exit Time and the Dividend Value Function for One-Dimensional Diffusion Processes Abstract and Applied Analysis |
| title | The Exit Time and the Dividend Value Function for
One-Dimensional Diffusion Processes |
| title_full | The Exit Time and the Dividend Value Function for
One-Dimensional Diffusion Processes |
| title_fullStr | The Exit Time and the Dividend Value Function for
One-Dimensional Diffusion Processes |
| title_full_unstemmed | The Exit Time and the Dividend Value Function for
One-Dimensional Diffusion Processes |
| title_short | The Exit Time and the Dividend Value Function for
One-Dimensional Diffusion Processes |
| title_sort | exit time and the dividend value function for one dimensional diffusion processes |
| url | http://dx.doi.org/10.1155/2013/675202 |
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