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postgraduate thesis: Analysis of the generalized Gerber-Shiu function in discrete-time dependent Sparre Andersen model

TitleAnalysis of the generalized Gerber-Shiu function in discrete-time dependent Sparre Andersen model
Authors
Issue Date2016
PublisherThe University of Hong Kong (Pokfulam, Hong Kong)
Citation
Qi, X. [亓孝真]. (2016). Analysis of the generalized Gerber-Shiu function in discrete-time dependent Sparre Andersen model. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5719475
AbstractThere is a vast literature in the analysis of the insurer's surplus process under the Sparre Andersen risk model. Since it is cumbersome to calculate distributions of ruin-related quantities in the continuous-time model, we shall consider the discrete-time model as a quick approximation to the corresponding ones in the continuous-time model. In this work, we consider the discrete-time setting of the Sparre Andersen risk model and use the generalized Gerber-Shiu function to study various ruin-related quantities associated with variables in the generalized Gerber-Shiu function such as the ladder height and the claim causing ruin. First, the structural properties of the generalized Gerber-Shiu function are obtained and in turn, joint/marginal distributions of ruin-related quantities of our interest are derived. Then we shall assume particular dependency structure for the claim sizes and the interclaim times. In addition to the ordinary risk model, the delayed model has been receiving attention since the occurrence of the last claim before time zero is taken into account to model the process. Hence we shall investigate general results for the Gerber-Shiu function in the delayed model with time-dependent claim and also focus on its relationship with the ordinary model. Finally the Farlie-Gumbel-Mogenstern (FGM) copula is considered to model dependency structure and distributions of the ruin-related quantities such as the claim causing ruin and the last ladder height. We will demonstrate the effects of dependency parameters, initial surpluses, discounting factors on the aforementioned distributions. Moreover, the probability functions of those quantities under the ordinary model and the delayed model are compared.
DegreeMaster of Philosophy
SubjectRisk (Insurance) - Mathematical models
Dept/ProgramStatistics and Actuarial Science
Persistent Identifierhttp://hdl.handle.net/10722/223621

 

DC FieldValueLanguage
dc.contributor.authorQi, Xiaozhen-
dc.contributor.author亓孝真-
dc.date.accessioned2016-03-03T23:16:51Z-
dc.date.available2016-03-03T23:16:51Z-
dc.date.issued2016-
dc.identifier.citationQi, X. [亓孝真]. (2016). Analysis of the generalized Gerber-Shiu function in discrete-time dependent Sparre Andersen model. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5719475-
dc.identifier.urihttp://hdl.handle.net/10722/223621-
dc.description.abstractThere is a vast literature in the analysis of the insurer's surplus process under the Sparre Andersen risk model. Since it is cumbersome to calculate distributions of ruin-related quantities in the continuous-time model, we shall consider the discrete-time model as a quick approximation to the corresponding ones in the continuous-time model. In this work, we consider the discrete-time setting of the Sparre Andersen risk model and use the generalized Gerber-Shiu function to study various ruin-related quantities associated with variables in the generalized Gerber-Shiu function such as the ladder height and the claim causing ruin. First, the structural properties of the generalized Gerber-Shiu function are obtained and in turn, joint/marginal distributions of ruin-related quantities of our interest are derived. Then we shall assume particular dependency structure for the claim sizes and the interclaim times. In addition to the ordinary risk model, the delayed model has been receiving attention since the occurrence of the last claim before time zero is taken into account to model the process. Hence we shall investigate general results for the Gerber-Shiu function in the delayed model with time-dependent claim and also focus on its relationship with the ordinary model. Finally the Farlie-Gumbel-Mogenstern (FGM) copula is considered to model dependency structure and distributions of the ruin-related quantities such as the claim causing ruin and the last ladder height. We will demonstrate the effects of dependency parameters, initial surpluses, discounting factors on the aforementioned distributions. Moreover, the probability functions of those quantities under the ordinary model and the delayed model are compared.-
dc.languageeng-
dc.publisherThe University of Hong Kong (Pokfulam, Hong Kong)-
dc.relation.ispartofHKU Theses Online (HKUTO)-
dc.rightsThe author retains all proprietary rights, (such as patent rights) and the right to use in future works.-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subject.lcshRisk (Insurance) - Mathematical models-
dc.titleAnalysis of the generalized Gerber-Shiu function in discrete-time dependent Sparre Andersen model-
dc.typePG_Thesis-
dc.identifier.hkulb5719475-
dc.description.thesisnameMaster of Philosophy-
dc.description.thesislevelMaster-
dc.description.thesisdisciplineStatistics and Actuarial Science-
dc.description.naturepublished_or_final_version-

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