A New Multivariate Dependent Measure Of Aggregation Risk

In addition to attention investment income, the investors will also carry on the comparison to the uncertainty of future earnings when they carrying insurance or?nancial investment. In other words, that is the measure of the di?erent investment risk. When evaluating the aggregate risk, the risk analyst has to assume that the risk factors are independent of each other. As a matter of fact, owing to the relationship between risk factors, such processing will underrate the aggregate risk. We can consider the risk of dependence to re?ect the size of the aggregation of risk. Construction of risk models and theories have become dependent actuarial study of classical problems.Inspired by Dhaene et al.(2014), in this thesis we will use the weighted average to introduce a new multivariate dependence measure. Using the concept of new negative strongest dependency in Puccetti et al.(2014), the measure range can extended to negative dependency. The new dependence measure ρnuse dimensionality reduction reduces the di?culty of calculating and simpli?es the di?culty of comparing risk.This thesis mainly describes a new dependence measure and its properties. The thesis is divided into ?ve sections according to contents:Chapter 1 Introduction. We introduce the main contents of this thesis.Chapter 2 Preliminaries. We mainly introduce some commonly used mathematical symbols and the nature of the distribution function FX. Later on, we will use the property between convex order and sequence of the variance. Then gave the upper and the lower bounds for Fr′echet a simple instructions.Chapter 3 Extremal dependence. We introduce some concepts of extremal dependence, including the formal de?nition and nature of an extremal positive dependence.In dimension d = 2, a strongest negatively dependent concept, called a countermonotonic random vector. In dimension d ≥ 3, Fr’echet space meet di?erent conditions of the strongest negative dependence and concentrate the strongest negative dependence structure in any Fr′echet.Chapter 4 The dependence measure. By using the variance of sum of random vectors and dimension reduction ideas, we can de?ne new dependence measure ρn.Meanwhile, we also list some properties of the ρnand give a comparison between the new measure and other measures. It is also explicit to clear out the new measure’s application in herd behavior.Chapter 5 Summary. We give a summary about the new measure.