Ακριβείς υπολογισμοί και προσεγγίσεις με χρήση του πακέτου actuar στο συλλογικό πρότυπο και την θεωρία αξιοπιστίας χαρτοφυλακίου

Ανδρούτσος, Αλέξανδρος

Exact calculations and approximations in the collective risk model and credibility theory using the actuar package

Master Thesis

Author

Ανδρούτσος, Αλέξανδρος

Date

2024-11

Abstract

This thesis deals with fundamental and specialized issues in actuarial science and risk management, emphasizing both theoretical analysis and practical applications using the actuar package in R. The work examines in detail the theory of collective risk, ruin theory, portfolio credibility, and the implementation of these theories in real-world risk scenarios for insurance companies. In the first part of the thesis, the theory of collective risk is developed, which is a fundamental tool in actuarial science for understanding and predicting the potential losses that an insurance portfolio may face. Here, key mathematical concepts such as moment-generating functions, probability-generating functions, and Laplace transforms are analyzed, which allow for the calculation of the distribution of total losses. Furthermore, mixed-type distribution models and the relationships that connect generating functions with risk dispersion are examined, providing significant insights into calculating the total losses of a portfolio. The next chapter focuses on ruin theory, which examines the risk management arising from the dynamic relationship between reserves and claims. The classic Cramér-Lundberg model, one of the fundamental models used in actuarial science, is analyzed, which explores the stochastic process of an insurance company’s surplus. Mathematical expressions and inequalities related to the probability of ruin are thoroughly examined, and how risk management can reduce the likelihood of the company’s financial failure is explored. Additionally, there is a reference to reinsurance strategies, such as proportional reinsurance and excess of loss reinsurance, which allow for risk distribution and portfolio stabilization. Following is the chapter on portfolio credibility theory, where techniques and models are presented that allow for more accurate premium estimation. The Bühlmann and Bühlmann-Straub models, which are benchmarks in actuarial science aimed at optimizing premiums by considering both the individual experience of insured individuals and the collective data of the portfolio, are analyzed. Credibility theory provides solutions to the problem of premium estimation in uncertain situations, balancing the individual data of the insured with the overall experience of the portfolio. The final part of the thesis is dedicated to applications in R, using the actuar package, which is specifically designed for actuarial and statistical calculations in the field of risk management. In these applications, examples and methodologies are presented for calculating distributions, discretizing functions, and estimating total losses, offering actuaries the ability to simulate and analyze loss and ruin scenarios. Using the commands and tools of the actuar package, the thesis demonstrates how models can be created and adapted to assist in accurate calculations and improve risk management. Overall, this thesis provides a comprehensive overview of actuarial science and risk management techniques, focusing on both theoretical approaches and practical applications that are critical for the stability and sustainability of insurance companies. The methods presented aim to achieve precise forecasting and enhance the financial management of insurance portfolios, making this work a valuable resource for both professional actuaries and researchers in the field of actuarial science.

Postgraduate Studies Programme

Αναλογιστική Επιστήμη και Διαχείριση Κινδύνων

Department

Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

Number of pages

112

Language

Greek

URI

https://dione.lib.unipi.gr/xmlui/handle/unipi/17180
http://dx.doi.org/10.26267/unipi_dione/4603

Collections

Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

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Except where otherwise noted, this item's license is described as
Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα