The Same Monotonicity Of Elliptic Distribution And Its Application

In traditional risk theory, the individual risks of a portfolio are usually assumed to be mutually independent. In general, however, each vector on its own will have dependent components. On a foggy day all cars of a region have higher probability to be involved in an accident. During dry hot sumners, all wooden cottages are more exposed to fire. The individual risks of an earthquake or flooding risk portfolio which are located in the some geographic area are correlated,since individual claims are contingent on the occurrence andseverity of the same、carthquake or flood. And the pension, these persons work at the same location, they take the same flights. It is evident that the mortality of these persons will be dependent, at last, to a certain extent. Therefore, it’s very important for predicting risk to study comonotinicity. This thesis studies comonotonicity, it is divided into five chapters.The first chapter of this thesis introduces some dependent examples and the background of comonotonicity.The second chapter of this thesis first introduces the definition and the theory of distri-bution function and the inverse of a. distribution function, then it introduces the definitions and the theory of comonotonicity.The third chapter of this thesis first introduces the definition and the theory of cornono-tinic sum, and we find some examples that their comonotonic sums (product) are closed,finding elliptical distributions satisfy that their comonotonic sums are closed, and log ellip-tical distributions satisfying that their comonotonic product are closed. A discrete example:the comonotonic sum of geometric distribution isn’t closed. So it is not true that all the functions satisfy that their comonotonic sums (product) are closed.The fourth chapter of this thesis introduces some correlation order theory.The fifth chapter of this thesis is the summary.