Applications the dependent risk models in the analysis of insurance portfolios

Anna Nikodem-Słowikowska

Abstract

The aim of the doctoral thesis is to describe the risk models with various dependent structure, and to present the methods of computation of the aggregate claims distribution for dependent risks model. The main objective is the analysis of the influence of dependence on the aggregate claims distribution and premiums. The dissertation consists of four chapters. The first chapter contains the description of the classical risk model (individual and collective) and of the models with various dependent structure. In the next chapter, the methods of computation of the aggregate claims distribution for described models are presented. Beside the methods which are mentioned in the professional literature, original methods are proposed. Described methods include: analytical method, recursive method, approximation and inversion method. In this chapter it is shown that the methods used in the classical risk models can be also applied to some dependent risk models. The third chapter concerns the selected premium principles which are used in the analysis of the impact of the dependence on the value of premium. The last chapter is the main part of the dissertation. This chapter presents the analysis which shows how dependence risk influences the shape of the aggregate claims distribution and the value of the premium. Many examples that confirm that this influence is significant are presented.
Diploma typeDoctor of Philosophy
Author Anna Nikodem-Słowikowska
Anna Nikodem-Słowikowska,,
-
Title in EnglishApplications the dependent risk models in the analysis of insurance portfolios
Languagepl polski
Certifying UnitFaculty of Management, Information Systems and Finance (MISaF)
Disciplineekonomia / nauki ekonomiczne(nauki ekonomiczne) / nauki społeczne()
Defense Date16-10-2013
End date17-10-2013
Supervisor Stanisław Heilpern (MISaF / IZM / KS)
Stanisław Heilpern,,
- Katedra Statystyki

Internal reviewers Zbigniew Michna (MISaF / IZM / KMiC)
Zbigniew Michna,,
- Katedra Matematyki i Cybernetyki
External reviewers Włodzimierz Szkutnik
Włodzimierz Szkutnik,,
-
Pages205
Keywords in Englishindividual and collective risk model, dependent risks, aggregate claims distribution, premium
Abstract in EnglishThe aim of the doctoral thesis is to describe the risk models with various dependent structure, and to present the methods of computation of the aggregate claims distribution for dependent risks model. The main objective is the analysis of the influence of dependence on the aggregate claims distribution and premiums. The dissertation consists of four chapters. The first chapter contains the description of the classical risk model (individual and collective) and of the models with various dependent structure. In the next chapter, the methods of computation of the aggregate claims distribution for described models are presented. Beside the methods which are mentioned in the professional literature, original methods are proposed. Described methods include: analytical method, recursive method, approximation and inversion method. In this chapter it is shown that the methods used in the classical risk models can be also applied to some dependent risk models. The third chapter concerns the selected premium principles which are used in the analysis of the impact of the dependence on the value of premium. The last chapter is the main part of the dissertation. This chapter presents the analysis which shows how dependence risk influences the shape of the aggregate claims distribution and the value of the premium. Many examples that confirm that this influence is significant are presented.
KBN classificationekonomia
Thesis file
Praca doktorska.pdf 4,29 MB
Other files
Opis rozprawy doktorskiej.pdf 123,79 KB

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