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Article: On a Gerber–Shiu type function and its applications in a dual semi-Markovian risk model
Title | On a Gerber–Shiu type function and its applications in a dual semi-Markovian risk model |
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Authors | |
Keywords | Dual risk model Generalized penalty function Gerber-Shiu function Last inter-arrival time Perpetual insurance Semi-Markovian risk process |
Issue Date | 2014 |
Publisher | Elsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/amc |
Citation | Applied Mathematics and Computation, 2014, v. 247, p. 1183-1201 How to Cite? |
Abstract | In this paper, we consider a dual risk process which can be used to model the surplus of a business that invests money constantly and earns gains randomly in both time and amount. The occurrences of the gains and their amounts are assumed follow a semi-Markovian structure (e.g. Reinhard (1984)). We analyze a quantity resembling the Gerber-Shiu expected discounted penalty function (Gerber and Shiu (1998)) that incorporates random variables defined before and after the time of ruin, such as the minimum surplus level before ruin and the time of the first gain after ruin. General properties of the function are studied, and some exact results are derived upon exponential distributional assumptions on either the inter-arrival times or the gain amounts. Applications in a perpetual insurance and the last inter-arrival time containing the time of ruin are given along with some numerical examples. |
Persistent Identifier | http://hdl.handle.net/10722/214571 |
ISSN | 2023 Impact Factor: 3.5 2023 SCImago Journal Rankings: 1.026 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Liu, L | - |
dc.contributor.author | Cheung, ECK | - |
dc.date.accessioned | 2015-08-21T11:38:17Z | - |
dc.date.available | 2015-08-21T11:38:17Z | - |
dc.date.issued | 2014 | - |
dc.identifier.citation | Applied Mathematics and Computation, 2014, v. 247, p. 1183-1201 | - |
dc.identifier.issn | 0096-3003 | - |
dc.identifier.uri | http://hdl.handle.net/10722/214571 | - |
dc.description.abstract | In this paper, we consider a dual risk process which can be used to model the surplus of a business that invests money constantly and earns gains randomly in both time and amount. The occurrences of the gains and their amounts are assumed follow a semi-Markovian structure (e.g. Reinhard (1984)). We analyze a quantity resembling the Gerber-Shiu expected discounted penalty function (Gerber and Shiu (1998)) that incorporates random variables defined before and after the time of ruin, such as the minimum surplus level before ruin and the time of the first gain after ruin. General properties of the function are studied, and some exact results are derived upon exponential distributional assumptions on either the inter-arrival times or the gain amounts. Applications in a perpetual insurance and the last inter-arrival time containing the time of ruin are given along with some numerical examples. | - |
dc.language | eng | - |
dc.publisher | Elsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/amc | - |
dc.relation.ispartof | Applied Mathematics and Computation | - |
dc.rights | © 2014. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ | - |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.subject | Dual risk model | - |
dc.subject | Generalized penalty function | - |
dc.subject | Gerber-Shiu function | - |
dc.subject | Last inter-arrival time | - |
dc.subject | Perpetual insurance | - |
dc.subject | Semi-Markovian risk process | - |
dc.title | On a Gerber–Shiu type function and its applications in a dual semi-Markovian risk model | - |
dc.type | Article | - |
dc.identifier.email | Cheung, ECK: eckc@hku.hk | - |
dc.identifier.authority | Cheung, ECK=rp01423 | - |
dc.description.nature | postprint | - |
dc.identifier.doi | 10.1016/j.amc.2014.09.059 | - |
dc.identifier.scopus | eid_2-s2.0-84908457124 | - |
dc.identifier.hkuros | 246147 | - |
dc.identifier.volume | 247 | - |
dc.identifier.spage | 1183 | - |
dc.identifier.epage | 1201 | - |
dc.identifier.isi | WOS:000344474800102 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 0096-3003 | - |