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Article: On optimality of the barrier strategy for a general Lévy risk process

TitleOn optimality of the barrier strategy for a general Lévy risk process
Authors
KeywordsBarrier strategy
Complete monotonicity
Lévy processes
Optimal dividend problem
Probability of ruin
Scale function
Issue Date2011
PublisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/mcm
Citation
Mathematical And Computer Modelling, 2011, v. 53 n. 9-10, p. 1700-1707 How to Cite?
AbstractWe consider the optimal dividend problem for the insurance risk process in a general Lévy process setting. The objective is to find a strategy which maximizes the expected total discounted dividends until the time of ruin. We give sufficient conditions under which the optimal strategy is of barrier type. In particular, we show that if the Lévy density is a completely monotone function, then the optimal dividend strategy is a barrier strategy. This approach was inspired by the work of Avram et al. [F. Avram, Z. Palmowski, M.R. Pistorius, On the optimal dividend problem for a spectrally negative Lévy process, The Annals of Applied Probability 17 (2007) 156-180], Loeffen [R. Loeffen, On optimality of the barrier strategy in De Finetti's dividend problem for spectrally negative Lévy processes, The Annals of Applied Probability 18 (2008) 1669-1680] and Kyprianou et al. [A.E. Kyprianou, V. Rivero, R. Song, Convexity and smoothness of scale functions with applications to De Finetti's control problem, Journal of Theoretical Probability 23 (2010) 547-564] in which the same problem was considered under the spectrally negative Lévy processes setting. © 2010 Elsevier Ltd.
Persistent Identifierhttp://hdl.handle.net/10722/135497
ISSN
2015 Impact Factor: 1.366
2015 SCImago Journal Rankings: 0.643
ISI Accession Number ID
Funding AgencyGrant Number
National Natural Science Foundation of China10771119
Research Fund for the Doctoral Program of Higher Education of China20093705110002
Funding Information:

We would like to thank the two anonymous referees who gave us many constructive suggestions and valuable comments on the previous version of this paper. The research of Kam C. Yuen was supported by a university research grant of the University of Hong Kong. The research of Chuancun Yin was supported by the National Natural Science Foundation of China (No. 10771119) and the Research Fund for the Doctoral Program of Higher Education of China ( No. 20093705110002).

References

 

DC FieldValueLanguage
dc.contributor.authorYuen, KCen_HK
dc.contributor.authorYin, Cen_HK
dc.date.accessioned2011-07-27T01:36:06Z-
dc.date.available2011-07-27T01:36:06Z-
dc.date.issued2011en_HK
dc.identifier.citationMathematical And Computer Modelling, 2011, v. 53 n. 9-10, p. 1700-1707en_HK
dc.identifier.issn0895-7177en_HK
dc.identifier.urihttp://hdl.handle.net/10722/135497-
dc.description.abstractWe consider the optimal dividend problem for the insurance risk process in a general Lévy process setting. The objective is to find a strategy which maximizes the expected total discounted dividends until the time of ruin. We give sufficient conditions under which the optimal strategy is of barrier type. In particular, we show that if the Lévy density is a completely monotone function, then the optimal dividend strategy is a barrier strategy. This approach was inspired by the work of Avram et al. [F. Avram, Z. Palmowski, M.R. Pistorius, On the optimal dividend problem for a spectrally negative Lévy process, The Annals of Applied Probability 17 (2007) 156-180], Loeffen [R. Loeffen, On optimality of the barrier strategy in De Finetti's dividend problem for spectrally negative Lévy processes, The Annals of Applied Probability 18 (2008) 1669-1680] and Kyprianou et al. [A.E. Kyprianou, V. Rivero, R. Song, Convexity and smoothness of scale functions with applications to De Finetti's control problem, Journal of Theoretical Probability 23 (2010) 547-564] in which the same problem was considered under the spectrally negative Lévy processes setting. © 2010 Elsevier Ltd.en_HK
dc.languageengen_US
dc.publisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/mcmen_HK
dc.relation.ispartofMathematical and Computer Modellingen_HK
dc.subjectBarrier strategyen_HK
dc.subjectComplete monotonicityen_HK
dc.subjectLévy processesen_HK
dc.subjectOptimal dividend problemen_HK
dc.subjectProbability of ruinen_HK
dc.subjectScale functionen_HK
dc.titleOn optimality of the barrier strategy for a general Lévy risk processen_HK
dc.typeArticleen_HK
dc.identifier.emailYuen, KC: kcyuen@hku.hken_HK
dc.identifier.authorityYuen, KC=rp00836en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.mcm.2010.12.042en_HK
dc.identifier.scopuseid_2-s2.0-79951942228en_HK
dc.identifier.hkuros187083en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-79951942228&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume53en_HK
dc.identifier.issue9-10en_HK
dc.identifier.spage1700en_HK
dc.identifier.epage1707en_HK
dc.identifier.isiWOS:000287729700012-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridYuen, KC=7202333703en_HK
dc.identifier.scopusauthoridYin, C=7201995678en_HK
dc.identifier.citeulike8627681-

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