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postgraduate thesis: On discrete-time risk models with dependence based on integer-valued time series processes

TitleOn discrete-time risk models with dependence based on integer-valued time series processes
Authors
Advisors
Advisor(s):Yuen, KC
Issue Date2012
PublisherThe University of Hong Kong (Pokfulam, Hong Kong)
Citation
Li, J. [黎嘉慧]. (2012). On discrete-time risk models with dependence based on integer-valued time series processes. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4852187
AbstractIn the actuarial literature, dependence structures in risk models have been extensively studied. The main theme of this thesis is to investigate some discrete-time risk models with claim numbers modeled by integer-valued time series processes. The first model is a common shock risk model with temporal dependence between the claim numbers in each individual class of business. Specifically the Poisson MA(1) process and Poisson AR(1) process are considered for the temporal dependence. To study the ruin probability, the equations associated with the adjustment coefficients are derived. Comparisons are also made to assess the impact of the dependence structures on the ruin probability. Another model involving both the correlated classes of business and the time series approach is then studied. Thinning dependence structure is adopted to model the dependence among classes of business. The Poisson MA(1) and Poisson AR(1) processes are used to describe the claim-number processes. Adjustment coefficients and ruin probabilities are examined. Finally a discrete-time risk model with the claim number following a Poisson ARCH process is proposed. In this model, the mean of the current claim number depends on the previous observations. Within this framework, the equation for finding the adjustment coefficient is derived. Numerical studies are also carried out to examine the effect of the Poisson ARCH dependence structure on several risk measures including ruin probability, Value at Risk, and conditional tail expectation.
DegreeMaster of Philosophy
SubjectRisk (Insurance) - Statistical methods.
Time-series analysis
Dept/ProgramStatistics and Actuarial Science

 

DC FieldValueLanguage
dc.contributor.advisorYuen, KC-
dc.contributor.authorLi, Jiahui-
dc.contributor.author黎嘉慧-
dc.date.issued2012-
dc.identifier.citationLi, J. [黎嘉慧]. (2012). On discrete-time risk models with dependence based on integer-valued time series processes. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4852187-
dc.description.abstractIn the actuarial literature, dependence structures in risk models have been extensively studied. The main theme of this thesis is to investigate some discrete-time risk models with claim numbers modeled by integer-valued time series processes. The first model is a common shock risk model with temporal dependence between the claim numbers in each individual class of business. Specifically the Poisson MA(1) process and Poisson AR(1) process are considered for the temporal dependence. To study the ruin probability, the equations associated with the adjustment coefficients are derived. Comparisons are also made to assess the impact of the dependence structures on the ruin probability. Another model involving both the correlated classes of business and the time series approach is then studied. Thinning dependence structure is adopted to model the dependence among classes of business. The Poisson MA(1) and Poisson AR(1) processes are used to describe the claim-number processes. Adjustment coefficients and ruin probabilities are examined. Finally a discrete-time risk model with the claim number following a Poisson ARCH process is proposed. In this model, the mean of the current claim number depends on the previous observations. Within this framework, the equation for finding the adjustment coefficient is derived. Numerical studies are also carried out to examine the effect of the Poisson ARCH dependence structure on several risk measures including ruin probability, Value at Risk, and conditional tail expectation.-
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.source.urihttp://hub.hku.hk/bib/B48521875-
dc.subject.lcshRisk (Insurance) - Statistical methods.-
dc.subject.lcshTime-series analysis-
dc.titleOn discrete-time risk models with dependence based on integer-valued time series processes-
dc.typePG_Thesis-
dc.identifier.hkulb4852187-
dc.description.thesisnameMaster of Philosophy-
dc.description.thesislevelMaster-
dc.description.thesisdisciplineStatistics and Actuarial Science-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.5353/th_b4852187-
dc.date.hkucongregation2012-

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