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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