Σύγκριση της πιθανότητας χρεοκοπίας για το κλασσικό μοντέλο της θεωρίας κινδύνων με και χωρίς διαχυτικό παράγοντα

Ψαρουδάκης, Ευστράτιος

Master Thesis

Author

Ψαρουδάκης, Ευστράτιος

Date

2026-03

Abstract

Collective Risk Theory constitutes a fundamental field of actuarial science and focuses on the stochastic modeling of the evolution of the surplus of insurance portfolios. A central quantity in this theory is the ruin probability, which presents the probability that the surplus become negative at some point in time. Within this framework, the development and comparison of different models, such as the classical model and the model perturbed by diffusion, are of particular importance for the accurate assessment of risk. In the present study, the ruin probability is examined in both the classical risk model and the model perturbed by diffusion, with the aim of performing a comparative analysis under common parameters. The analysis is conducted for different claim size distributions, specifically the exponential distribution and mixtures of exponential distributions, while maintaining the same mean claim size. The computation of the ruin probability is based on analytical methods and closed-form expressions where available, And the results are presented for discrete values of their initial surplus. In order to compare the two models, the ratio of the corresponding ruin probabilities are also employed, serving as a quantitative measure of the impact of diffusion. The analysis is carried out through the application of the corresponding computational methods for each model and distribution, while the results are compared for different values of the initial surplus using tables and graphical representations. The results indicate that the introduction of diffusion affects the behavior of the ruin probability, while the form of the claim size there is distribution plays a significant role in shaping the outcomes.

Postgraduate Studies Programme

Αναλογιστική Επιστήμη και Διαχείριση Κινδύνων

Department

Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

Number of pages

Language

Greek

URI

https://dione.lib.unipi.gr/xmlui/handle/unipi/19154

Collections

Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

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