Study On The Ruin Probability Of Insurance Risk Model With Dependent Heavy-tailed Claims

As an important branch of applied research in probability and statistics, the impact of risk theory should not be ignored with the development of the society. Generally speaking, the claim sizes caused by the major natural disasters, such as earthquakes, tsunami, hurricanes and other phenomena, are described by heavy-tailed distributions in risk theory. The probabilities of occurrence of these events are so small that it difficult to predict. However, insurance companies would bear huge losses if they were occurred, such risk models are consequently attracted broad attention of researchers in applied probability in recent years. Recently, a new trend of research in risk models with heavy-tailed distribution is to introduce varieties of dependent structures, which making correspond to the actual operations of insur-ance companies. On the other hand, as another topic of the applied probability, large deviation theory plays a vital role in quantitatively depicting extremal events. Because of the importance of heavy-tailed distributions in finance and insurance, and lots of problems in which can be boiled down to one of large deviations, the large deviation problems of random sums and partial sums of heavy-tailed random variables are also worth paying attention. On the basis of insurance risk theory based on policy entrance process contributes to Li et al (2005), in this thesis, we constructed a model with constant interest force by considering the surplus process in economic environment, the ruin probability and precisely large deviations were eventually studied. The thesis contains 4 chapters, chapter 1 firstly presented the background and value of the paper, then reviewed the history of classical Cramer-Lundberg risk model and its ruin probability, after that, heavy-tailed distributions and some depen-dent structures were summarized, research actuality and the trend of development of the insurance risk model were finally expounded and the various generalizations of the classical risk model were stated.Chapter 2 considered the insurance risk model with constant interest force based on policy entrance process, in which assumed that the distributions of claim sizes belongs to D in the presence of pairwise quasi-asymptotical independence, the con-sistently asymptotical expressions of finite time and infinite horizon ruin probability were finally derived and some numerical results were given to access the qualities of the asymptotic relations, specially, when distributions of the claim sizes belongs to C, the asymptotical equalities were obtained.Chapter 3 investigated the precisely large deviations of the loss process based on the customer-arriving risk model, in which claim sizes were assumed to be neg-atively quadrant dependent, identically distributed and belonged to heavy-tailed distribution class L?D.Chapter 4 summarized the work of the thesis and provided an outlook for further study.