Λοξές κατανομές στα χρηματοοικονομικά και στην αναλογιστική επιστήμη

Abstract

In this diploma thesis that will follow, we look at the skew distributions, distributions of which one tail is wider, something that is usually observed in portfolio analysis. Based on the study of Adelchi Azzalini and Antonella Capitanio (The Skew-Normal and Related Families (2014)) on skew distributions, we will study probability distributions which can predict low probability risks but with high losses. Specifically, in the first chapter we get acquainted with the basic known probability distributions by analyzing the probability function, basic properties, mean value, variance and we present the necessary diagrams. In the same chapter there is an extensive reference of the most important statistical method of parameter estimation, the method of maximum likelihood, as well as an introduction to skewness through some important definitions and propositions. In the second chapter, there is a detailed study and analysis of skewed distributions in terms of probability density function, distribution function, basic descriptive measures such as mean, variance, skewness and kurtosis, important properties that govern them, diagrams and standard functions to estimate the parameters of each skew distribution . The skew distributions to be studied are the Skew Normal, Skew Students-t, Beta Skew t, Skew Logistic, and Skew Cauchy. Lastly, in the third chapter with the help of the programming language R the skew distributions will be applied and compared with other known distributions on real data to be able to draw conclusions.