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postgraduate thesis: On the joint analysis of discounted aggregate claim costs until ruin and other ruinrelated quantities
Title  On the joint analysis of discounted aggregate claim costs until ruin and other ruinrelated quantities 

Authors  
Issue Date  2015 
Publisher  The University of Hong Kong (Pokfulam, Hong Kong) 
Citation  Liu, H. [劉海波]. (2015). On the joint analysis of discounted aggregate claim costs until ruin and other ruinrelated quantities. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5576759 
Abstract  In the context of classical ruin theory, ruin quantities (e.g. ruin probability and the time of ruin) are studied separately. It was not until the publication of the seminal paper by Gerber and Shiu (1998) that researchers began to focus on the joint analysis of several ruin quantities. Gerber and Shiu (1998) proposed the wellknown GerberShiu expected discounted penalty function or GerberShiu function which unifies the study of three key ruin quantities, namely the time of ruin, the surplus just before ruin and the deficit at ruin. In this thesis, we further incorporate the discounted aggregate claim costs until ruin as well as the discounted aggregate dividends until ruin if any dividend strategy is implemented into the GerberShiu function. The generalized GerberShiu function is examined under the compound Poisson model with a barrier dividend strategy or a threshold dividend strategy and a risk model with 2sided jumps.
In a risk model with a barrier dividend strategy or a threshold dividend strategy, dividends are paid to shareholder whenever the surplus reaches a predetermined level. The dividends and the claims can be deemed as the payments to the shareholders and policyholders, respectively. As it will be seen in this thesis, if the cost function is specified, the generalized GerberShiu function allows us study the time of ruin, the discounted total dividends until ruin and the discounted aggregate claims until ruin at the same time. Numerical examples are also provided to illustrate the relationship between these quantities.
In traditional risk models, insurance companies are assumed to receive premiums at a constant rate. However, some premiums are paid in lump sums, such as insurances of traveling art collections. The assumptions in a risk model with 2sided jumps are more realistic in this regard since the upward jumps represent the random premiums. To separate the contributions of random gains and losses, both the discounted aggregate downward jump `costs' until ruin and the discounted aggregate upward jump `costs' until ruin are incorporated into the GerberShiu function. Aside from the general analysis of the generalized GerberShiu function, explicit solutions of two special cases under specific downward jump distribution assumptions are derived along with numerical illustrations related to the first case. 
Degree  Master of Philosophy 
Subject  Risk (Insurance)  Mathematical models 
Dept/Program  Statistics and Actuarial Science 
Persistent Identifier  http://hdl.handle.net/10722/231097 
HKU Library Item ID  b5576759 
DC Field  Value  Language 

dc.contributor.author  Liu, Haibo   
dc.contributor.author  劉海波   
dc.date.accessioned  20160902T23:37:32Z   
dc.date.available  20160902T23:37:32Z   
dc.date.issued  2015   
dc.identifier.citation  Liu, H. [劉海波]. (2015). On the joint analysis of discounted aggregate claim costs until ruin and other ruinrelated quantities. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5576759   
dc.identifier.uri  http://hdl.handle.net/10722/231097   
dc.description.abstract  In the context of classical ruin theory, ruin quantities (e.g. ruin probability and the time of ruin) are studied separately. It was not until the publication of the seminal paper by Gerber and Shiu (1998) that researchers began to focus on the joint analysis of several ruin quantities. Gerber and Shiu (1998) proposed the wellknown GerberShiu expected discounted penalty function or GerberShiu function which unifies the study of three key ruin quantities, namely the time of ruin, the surplus just before ruin and the deficit at ruin. In this thesis, we further incorporate the discounted aggregate claim costs until ruin as well as the discounted aggregate dividends until ruin if any dividend strategy is implemented into the GerberShiu function. The generalized GerberShiu function is examined under the compound Poisson model with a barrier dividend strategy or a threshold dividend strategy and a risk model with 2sided jumps. In a risk model with a barrier dividend strategy or a threshold dividend strategy, dividends are paid to shareholder whenever the surplus reaches a predetermined level. The dividends and the claims can be deemed as the payments to the shareholders and policyholders, respectively. As it will be seen in this thesis, if the cost function is specified, the generalized GerberShiu function allows us study the time of ruin, the discounted total dividends until ruin and the discounted aggregate claims until ruin at the same time. Numerical examples are also provided to illustrate the relationship between these quantities. In traditional risk models, insurance companies are assumed to receive premiums at a constant rate. However, some premiums are paid in lump sums, such as insurances of traveling art collections. The assumptions in a risk model with 2sided jumps are more realistic in this regard since the upward jumps represent the random premiums. To separate the contributions of random gains and losses, both the discounted aggregate downward jump `costs' until ruin and the discounted aggregate upward jump `costs' until ruin are incorporated into the GerberShiu function. Aside from the general analysis of the generalized GerberShiu function, explicit solutions of two special cases under specific downward jump distribution assumptions are derived along with numerical illustrations related to the first case.   
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: Attribution 3.0 Hong Kong License   
dc.subject.lcsh  Risk (Insurance)  Mathematical models   
dc.title  On the joint analysis of discounted aggregate claim costs until ruin and other ruinrelated quantities   
dc.type  PG_Thesis   
dc.identifier.hkul  b5576759   
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_b5576759   