# Estimation of the Tail Dependence Coefficient

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http://urn.fi/URN:NBN:fi:hulib-202109293769
 Julkaisun nimi: Estimation of the Tail Dependence Coefficient Tekijä: Sohkanen, Pekka Muu tekijä: Helsingin yliopisto, Matemaattis-luonnontieteellinen tiedekunta University of Helsinki, Faculty of Science Helsingfors universitet, Matematisk-naturvetenskapliga fakulteten Julkaisija: Helsingin yliopisto Päiväys: 2021 Kieli: eng URI: http://urn.fi/URN:NBN:fi:hulib-202109293769 http://hdl.handle.net/10138/334691 Opinnäytteen taso: pro gradu -tutkielmat Koulutusohjelma: Matematiikan ja tilastotieteen maisteriohjelma Master's Programme in Mathematics and Statistics Magisterprogrammet i matematik och statistik Opintosuunta: Sovellettu matematiikka Applied Mathematics Tillämpad matematik Tiivistelmä: The fields of insurance and financial mathematics require increasingly intricate descriptors of dependency. In the realm of financial mathematics, this demand arises from globalisation effects over the past decade, which have caused financial asset returns to exhibit increasingly intricate dependencies between each other. Of particular interest are measurements describing the probabilities of simultaneous occurrences between unusually negative stock returns. In insurance mathematics, the ability to evaluate probabilities associated with the simultaneous occurrence of unusually large claim amounts can be crucial for both the solvency and the competitiveness of an insurance company. These sorts of dependencies are referred to by the term tail dependence. In this thesis, we introduce the concept of tail dependence and the tail dependence coefficient, a tool for determining the amount of tail dependence between random variables. We also present statistical estimators for the tail dependence coefficient. Favourable properties of these estimators are investigated and a simulation study is executed in order to evaluate and compare estimator performance under a variety of distributions. Some necessary stochastics concepts are presented. Mathematical models of dependence are introduced. Elementary notions of extreme value theory and empirical processes are touched on. These motivate the presented estimators and facilitate the proofs of their favourable properties. Avainsanat: tail dependence tail dependence coefficient tail dependence estimation
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