Ιδιότητες και προσεγγίσεις για μείξεις και συνελίξεις γάμμα κατανομών

Τριαντοπούλου, Ελένη

Properties and approximations for mixtures and convolutions of gamma distributions

Master Thesis

Author

Τριαντοπούλου, Ελένη

Date

2020-12

Abstract

Actuarial Science is a branch of applied and financial mathematics which has nowadays developed rapidly in the field of insurance. Specifically, bankruptcy theory, as one of the most important branches of risk theory, studies the evolution of the surplus, id est the changes in the income and the expenses over time for an insurance portfolio. Moreover, it is particularly essential to model the amounts of compensation in the model of collective risk and select the appropriate distributions for the description of both individual sizes and total losses. Over many years, Gamma distribution which is a continuous distribution with two parameters (scale and shape), is widely used not only in statistical analysis but also in the field of actuarial science. They are distributions that have now been studied in detail and for this reason are widely applied in the modeling of insurance portfolios. Nevertheless, the mixtures and the convolutions of these distributions are of particular interest for the actuarial science and risk management. For the purpose of this thesis, we will try to investigate through examples the asymmetry and the kurtosis for the mixtures and the convolutions of Gamma distributions in order to analyze their shape and identify what combinations of parameters and weights (for mixtures only) give us specific characteristics respectively. At the same time, we will attempt to approach the convolution of Gamma distributions through other distributions because it is widely known that convolutions of Gamma do not always have a closed form and we will also study their application in the risk theory and the collective model of portfolios.

Postgraduate Studies Programme

Αναλογιστική Επιστήμη και Διοικητική Κινδύνου

Department

Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

Number of pages

150

Language

Greek

URI

https://dione.lib.unipi.gr/xmlui/handle/unipi/13145
http://dx.doi.org/10.26267/unipi_dione/568

Collections

Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

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