# Estimation of the Tail Dependence Coefficient

 dc.contributor Helsingin yliopisto, Matemaattis-luonnontieteellinen tiedekunta fi dc.contributor University of Helsinki, Faculty of Science en dc.contributor Helsingfors universitet, Matematisk-naturvetenskapliga fakulteten sv dc.contributor.author Sohkanen, Pekka dc.date.issued 2021 dc.identifier.uri URN:NBN:fi:hulib-202109293769 dc.identifier.uri http://hdl.handle.net/10138/334691 dc.description.abstract 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. en 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. dc.language.iso eng dc.publisher Helsingin yliopisto fi dc.publisher University of Helsinki en dc.publisher Helsingfors universitet sv dc.subject tail dependence dc.subject tail dependence coefficient dc.subject tail dependence estimation dc.title Estimation of the Tail Dependence Coefficient en dc.type.ontasot pro gradu -tutkielmat fi dc.type.ontasot master's thesis en dc.type.ontasot pro gradu-avhandlingar sv dct.identifier.urn URN:NBN:fi:hulib-202109293769 dc.subject.specialization Sovellettu matematiikka fi dc.subject.specialization Applied Mathematics en dc.subject.specialization Tillämpad matematik sv dc.subject.degreeprogram Matematiikan ja tilastotieteen maisteriohjelma fi dc.subject.degreeprogram Master's Programme in Mathematics and Statistics en dc.subject.degreeprogram Magisterprogrammet i matematik och statistik sv