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Article: A direct approach to the discounted penalty function
Title | A direct approach to the discounted penalty function |
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Authors | |
Issue Date | 2010 |
Publisher | Society of Actuaries. The Journal's web site is located at http://www.tandfonline.com/loi/uaaj20#.VP8_TPldX5E |
Citation | North American Actuarial Journal, 2010, v. 14 n. 4, p. 420-434 How to Cite? |
Abstract | This paper provides a new and accessible approach to establishing certain results concerning the discounted penalty function. The direct approach consists of two steps. In the first step, closedform expressions are obtained in the special case in which the claim amount distribution is a combination of exponential distributions. A rational function is useful in this context. For the second step, one observes that the family of combinations of exponential distributions is dense. Hence, it suffices to reformulate the results of the first step to obtain general results. The surplus process has downward and upward jumps, modeled by two independent compound Poisson processes. If the distribution of the upward jumps is exponential, a series of new results can be obtained with ease. Subsequently, certain results of Gerber and Shiu [H. U. Gerber and E. S. W. Shiu, North American Actuarial Journal 2(1): 48-78 (1998)] can be reproduced. The two-step approach is also applied when an independent Wiener process is added to the surplus process. Certain results are related to Zhang et al. [Z. Zhang, H. Yang, and S. Li, Journal of Computational and Applied Mathematics 233: 1773-1784 (2010)], which uses different methods. |
Persistent Identifier | http://hdl.handle.net/10722/135503 |
ISSN | 2023 Impact Factor: 1.4 2023 SCImago Journal Rankings: 0.692 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
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dc.contributor.author | Albrecher, H | en_HK |
dc.contributor.author | Gerber, HU | en_HK |
dc.contributor.author | Yang, H | en_HK |
dc.date.accessioned | 2011-07-27T01:36:09Z | - |
dc.date.available | 2011-07-27T01:36:09Z | - |
dc.date.issued | 2010 | en_HK |
dc.identifier.citation | North American Actuarial Journal, 2010, v. 14 n. 4, p. 420-434 | en_HK |
dc.identifier.issn | 1092-0277 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/135503 | - |
dc.description.abstract | This paper provides a new and accessible approach to establishing certain results concerning the discounted penalty function. The direct approach consists of two steps. In the first step, closedform expressions are obtained in the special case in which the claim amount distribution is a combination of exponential distributions. A rational function is useful in this context. For the second step, one observes that the family of combinations of exponential distributions is dense. Hence, it suffices to reformulate the results of the first step to obtain general results. The surplus process has downward and upward jumps, modeled by two independent compound Poisson processes. If the distribution of the upward jumps is exponential, a series of new results can be obtained with ease. Subsequently, certain results of Gerber and Shiu [H. U. Gerber and E. S. W. Shiu, North American Actuarial Journal 2(1): 48-78 (1998)] can be reproduced. The two-step approach is also applied when an independent Wiener process is added to the surplus process. Certain results are related to Zhang et al. [Z. Zhang, H. Yang, and S. Li, Journal of Computational and Applied Mathematics 233: 1773-1784 (2010)], which uses different methods. | en_HK |
dc.language | eng | en_US |
dc.publisher | Society of Actuaries. The Journal's web site is located at http://www.tandfonline.com/loi/uaaj20#.VP8_TPldX5E | en_HK |
dc.relation.ispartof | North American Actuarial Journal | en_HK |
dc.title | A direct approach to the discounted penalty function | en_HK |
dc.type | Article | en_HK |
dc.identifier.email | Yang, H: hlyang@hku.hk | en_HK |
dc.identifier.authority | Yang, H=rp00826 | en_HK |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1080/10920277.2010.10597599 | - |
dc.identifier.scopus | eid_2-s2.0-79954542362 | en_HK |
dc.identifier.hkuros | 187189 | en_US |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-79954542362&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 14 | en_HK |
dc.identifier.issue | 4 | en_HK |
dc.identifier.spage | 420 | en_HK |
dc.identifier.epage | 434 | en_HK |
dc.identifier.isi | WOS:000211868900004 | - |
dc.publisher.place | United States | en_HK |
dc.identifier.scopusauthorid | Albrecher, H=6602776321 | en_HK |
dc.identifier.scopusauthorid | Gerber, HU=7202185517 | en_HK |
dc.identifier.scopusauthorid | Yang, H=7406559537 | en_HK |
dc.identifier.issnl | 1092-0277 | - |