The Supremum Of Random Walk With Linearly Negative Quadrant Dependent And Heavy-tailed Steps

In daily life, unexpected things such as natural disasters and man-made accidents will bring unmeasurable loss and damage. These unforeseen unknown, is what we can call risk. Insurance is derived from the existence of risk. risk models applied in many fields, whose core question is the ruin probability of insurance company. In this paper, from the classical Cramer-Lundberg risk model, the Embrechts-Veraverbeke asymptotic expression is obtains that the supremum of linear negatively quadrant dependent (LNQD) random variables sequences in a limited amount of conditions for relaxing and promotion.This paper mainly divided into three chapters.Chapter1as the introduction, mainly introduced the research status and related background knowledge about the risk theory, from the domestic to overseas. And then, lead out the research contents of this thesis mainly.Chapter2is the preliminary knowledge, mainly introduced the model that need to prepare the related knowledge of risk theory. Classical Cramer-Lundberg risk model, Cramer Lundberg asymptotic expression and Lundberg upper bound are discussed in detail and instructions. Then, heavy-tailed distribution and the correlation function was analyzed, and corresponding conclusion is given. The last section is given of several common definition of independent random variables and their important properties. Exspecially, for the LNQD random variables sequence with a common heavy-tailed distribution which on the basic of the main theorem.Chapter3to prove the main theorem of this paper. This paper obtains the Embrechts-Veraverbeke asymptotic expression for the LNQD with heavy-tailed distibutiong such that its left tail is lighter than its right tail. As follows,In this paper, we improve the random variables with independence steps to the LNQD random variables sequence with heavy-tailed.