Ταυτότητες συνδιακύμανσης με εφαρμογές σε αναλογιστικά μέτρα κινδύνων

Μηλιάδης, Νικόλαος

Covariance identities with applications to actuarial risk measures

Master Thesis

Author

Μηλιάδης, Νικόλαος

Date

2021-06

Abstract

The main aim of this dissertation is to present three different generalizations of Stein’s identity, which refers to the relation between the covariance of a random variable X that follows the normal distribution and a random variable g(X). These generalizations are based on the papers of Papadatos and Papathanasiou (2001), Kattumanil (2009) and Landsman and Valdez (2016). Specifically, in the first chapter results from the work of Papadatos and Papathanasiou are studied and their applications in known distributions are investigated. Then, in the second chapter, another form of covariance identity due to Kattumanil is obtained, which is a generalization of the respective identities of Papadatos and Papathanasiou. Furthermore, applications of this generalized identity are given for families of distributions such as the well known Pearson family, while a connection is made with the Lorenz curve and the Gini index. In the third and final chapter, the paper of Landsman and Valdez is studied, and an extension of Stein’s identity for distribution tails is obtained. This identity is a useful tool in calculating tail conditional moments of random variables, which in turn appear often in actuarial risk management.

Postgraduate Studies Programme

Αναλογιστική Επιστήμη και Διοικητική Κινδύνου

Department

Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

Number of pages

Language

Greek

URI

https://dione.lib.unipi.gr/xmlui/handle/unipi/13730
http://dx.doi.org/10.26267/unipi_dione/1153

Collections

Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

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Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα