The Study of Precise Large Deviations of Risk Model with Dependent Heavy-tailed Claims
|School||Northwest Normal University|
|Course||Probability Theory and Mathematical Statistics|
|Keywords||heavy-tailed distribution negative dependence risk model classL∩D extended negatively dependent|
The thesis studies large deviations of heavy-tailed dependent risk model. Aseveryone knows, in the finance and insurance, the more attention is the extremeevents. Because these events don’t happen very often, but once it happens, it willbring great loss, resulting in the claims, which brings great risk to the insurancebusiness. In insurance all kinds of researches on the Asymptotic for ruin probabilitiesare much related to large deviation theory. So large deviation theory has caused wideconcern by many insurance companies and the scholars. Large deviation theoryoriginated in the1930s is always full of vigorous of a branch of the limit theory field.It plays a key role for the characterization of extreme events. After the researchof many scholars, has formed a series of characteristic research. The claims sizeprocess which is the main object, is not necessarily mutually independent, it canbe a kind of negatively dependent or other dependent process. Correspondingly,theinter-arrival time process is also not necessarily independent.The distribution of thenet loss caused by a claim is heavy-tailed. Our conclusions in this paper not onlyenriched theory of insurance risk, but also that achieved a value exploration onrelated theory application of the large deviation theoryThe thesis is divided into four chapters according to content. The first chapterintroduces some related knowledge of heavy-tailed distributions and dependencestructure.Chapter2studied the large deviation theory of heavy-tailed distribution whichincludes two aspects. The first knowledge of the outlines of large deviation theorywhich divided into classical large deviations and the precise large deviations. First,we summarized the theory of the classical large deviations and the precise large deviation,in order to make clear diference of them,then from the conditions of thestudy, the amount of research, the fine degree results representation and researchare made simple comparison.In the end,we summarized some results of the largedeviation. Last second details the main claims and the delay claims caused by itsdelay claims risk model. The insurance companies often experience delayed claim.For example,when a car accident occurs, the guarantor must not only pay the carloss, and, if the insured bought the third party liability insurance,guarantor also inthe random delay time for the third party payment. in earthquakes, hurricanesand other catastrophic risk usually have a lot of risk occurrence, some direct canhandle, but some need a certain period of time to resolve,and some of the risks maydelay (such as after the earthquake will cause many diseases, and these diseases aredue to random).Because of the reality of the model, and attracts the attention ofthe insurance company and the majority of scholars.Chapter3is the main results of the thesis. In the delayed claims risk models,itis extended to the heavy-tailed distribution and a series of dependent random vari-ables, and obtain the corresponding precise large deviation results. Further more,the heavy-tailed L D class,column is extended negative dependence of non-identically distributed for the first time applied to delayed claims risk model,andlarge deviations of the prospective-loss process is investigated.The conclusion notonly extended the single insurance risk model, but also enriched the existing litera-ture on the researched results of delayed claims risk model.The forth part summarizes this paper and gives an outlook for further study inthis field.