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postgraduate thesis: Analysis of some risk processes in ruin theory
Title  Analysis of some risk processes in ruin theory 

Authors  
Advisors  Advisor(s):Cheung, ECK 
Issue Date  2013 
Publisher  The University of Hong Kong (Pokfulam, Hong Kong) 
Citation  Liu, L. [劉綠茵]. (2013). Analysis of some risk processes in ruin theory. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5153734 
Abstract  In the literature of ruin theory, there have been extensive studies trying to generalize the classical insurance risk model. In this thesis, we look into two particular risk processes considering multidimensional risk and dependent structures respectively.
The first one is a bivariate risk process with a dividend barrier, which concerns a twodimensional risk model under a barrier strategy. Copula is used to represent the dependence between two business lines when a common shock strikes. By defining the time of ruin to be the first time that either of the two lines has its surplus level below zero, we derive a discrete approximation procedure to calculate the expected discounted dividends until ruin under such a model. A thorough discussion of application in proportional reinsurance with numerical examples is provided as well as an examination of the joint optimal dividend barrier for the bivariate process.
The second risk process is a semiMarkovian dual risk process. Assuming that the dependence among innovations and waiting times is driven by a Markov chain, we analyze a quantity resembling the GerberShiu expected discounted penalty function 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 distributional assumptions on either the interarrival times or the gain amounts. Applications in a perpetual insurance and the last interarrival time before ruin are given along with some numerical examples. 
Degree  Master of Philosophy 
Subject  Risk (Insurance)  Mathematical models 
Dept/Program  Statistics and Actuarial Science 
Persistent Identifier  http://hdl.handle.net/10722/195992 
HKU Library Item ID  b5153734 
DC Field  Value  Language 

dc.contributor.advisor  Cheung, ECK   
dc.contributor.author  Liu, Luyin   
dc.contributor.author  劉綠茵   
dc.date.accessioned  20140321T03:50:03Z   
dc.date.available  20140321T03:50:03Z   
dc.date.issued  2013   
dc.identifier.citation  Liu, L. [劉綠茵]. (2013). Analysis of some risk processes in ruin theory. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5153734   
dc.identifier.uri  http://hdl.handle.net/10722/195992   
dc.description.abstract  In the literature of ruin theory, there have been extensive studies trying to generalize the classical insurance risk model. In this thesis, we look into two particular risk processes considering multidimensional risk and dependent structures respectively. The first one is a bivariate risk process with a dividend barrier, which concerns a twodimensional risk model under a barrier strategy. Copula is used to represent the dependence between two business lines when a common shock strikes. By defining the time of ruin to be the first time that either of the two lines has its surplus level below zero, we derive a discrete approximation procedure to calculate the expected discounted dividends until ruin under such a model. A thorough discussion of application in proportional reinsurance with numerical examples is provided as well as an examination of the joint optimal dividend barrier for the bivariate process. The second risk process is a semiMarkovian dual risk process. Assuming that the dependence among innovations and waiting times is driven by a Markov chain, we analyze a quantity resembling the GerberShiu expected discounted penalty function 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 distributional assumptions on either the interarrival times or the gain amounts. Applications in a perpetual insurance and the last interarrival time before ruin are given along with some numerical examples.   
dc.language  eng   
dc.publisher  The University of Hong Kong (Pokfulam, Hong Kong)   
dc.relation.ispartof  HKU Theses Online (HKUTO)   
dc.rights  The author retains all proprietary rights, (such as patent rights) and the right to use in future works.   
dc.rights  Creative Commons: AttributionNonCommerical 3.0 Hong Kong License   
dc.subject.lcsh  Risk (Insurance)  Mathematical models   
dc.title  Analysis of some risk processes in ruin theory   
dc.type  PG_Thesis   
dc.identifier.hkul  b5153734   
dc.description.thesisname  Master of Philosophy   
dc.description.thesislevel  Master   
dc.description.thesisdiscipline  Statistics and Actuarial Science   
dc.description.nature  published_or_final_version   
dc.identifier.doi  10.5353/th_b5153734   