Regarding the relationships among different insurance claims, especially in
non-life insurance, the dependence behaviour in various models has been studied
extensively. In this thesis, some discrete-time risk models with dependence
structures would be investigated.
One traditional discrete-time risk model is the time series risk model, in
which the dependence would be on two aspects: time correlated claims and dependent
business classes. A general vector (multivariate) autoregressive moving
average (VARMA) model would be adopted to analyze the ruin probability
of a surplus process. An upper bound for the ruin probability is derived for the
general order of multivariate time series models in claims. Simulation studies
are carried out for model comparison for finite time ruin probabilities.
Another class of risk model is the compound binomial risk model, where the
dependence structure would be based on the existence of a so-called by-claim
in the claim process. The by-claim could be incurred in the same period as the
main insurance claim, or it would be incurred in the next period, depending
on a certain probability. A randomized dividend payment scheme with some
fixed threshold value in surplus level would also be considered in this thesis. A
methodology is discovered to obtain the Gerber-Shiu expected penalty function
for the extended model.
The final model investigated in this thesis is the periodic time series risk
model. The periodic structure of the model gives a practical interpretation
of the business cycle, in which there are high season and low season for the
business. Some lower order periodic time series models are considered for the
claim structures. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy
| Identifer | oai:union.ndltd.org:HKU/oai:hub.hku.hk:10722/174524 |
| Date | January 2012 |
| Creators | Wat, Kam-pui., 屈錦培. |
| Contributors | Li, WK, Yuen, KC |
| Publisher | The University of Hong Kong (Pokfulam, Hong Kong) |
| Source Sets | Hong Kong University Theses |
| Language | English |
| Detected Language | English |
| Type | PG_Thesis |
| Source | http://hub.hku.hk/bib/B47849666 |
| Rights | The author retains all proprietary rights, (such as patent rights) and the right to use in future works., Creative Commons: Attribution 3.0 Hong Kong License |
| Relation | HKU Theses Online (HKUTO) |
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