Study Of Heavy-Tailed Phenomenons Based On Financial And Insurance Fields

The main line of this paper is heavy-tailed phenomenon, we adopt the method of combining empirical analysis and theoretical analysis to study the phenomenons appear in financial and insurance fields.This paper first introduces the corresponding theoretical knowledge, In the fifth chapter, eight different kinds of stock market index yields of China and the U.S. are selected as research objects in order to analyze the heavy-tailed phenomenon in financial field. First, this part of context describes the tail features of data qualitatively and quantitatively through charts and heavy-tailed index. Then, we analyze the tail correlation between return series in the same industry of two countries. Time-varying SJC-Copula is chosen as the main research tool.Meanwhile the mapping effect is introduced between stock markets during analysis process. In addition, financial crisis is taken into account so that the data sample is divided into three sub-samples, and the paper gives concrete analyses for each part of data sample. Finally, we reach the following conclusions:the left side tail correlation coefficients of energy, industrial and financial industries are highter than that of right side, the basic material industry behaves in the opposite way. We only find left tail correlation in common consumer goods industry and the pharmaceuticals industry have low correlation on both sides of the tail. There is no tail correlation between two stock markets of the telecom and utility industries. The U.S. stock market have left tail mapping effect to Chinese stock market in the six industries which tail correlation exist, but we haven’t find any mapping effect in stock market from China to the U.S.. As a general view, the rise of tail correlation caused by financial crisis reveals that Chinese stock market is developing towards the mature stock market of the U.S..In the sixth chapter of this paper, we use theoretical analysis to study heavy-tailed phenomenons appear in insurance field. On the basis of classical risk model, we construct a local Max-Sum equivalence and proved it under the assumption that the claims of insurance company are subjected to local exponential distribution. And then we consider the ruin probability of a nonstandard bidmimensinal renewal risk model with two types of dependent structures. In this model, two kinds of claim sizes with heavy-tailed distributions are share the same arrival time, two kinds of Copula dependent structures are constructed on the basis of Farlie-Gumbel-Morgenstern structure. When these dependent structures are satisfied between the claim sizes and their inter-arrival times, we obtain two asymptotic formulas for ruin probabilities.