Υπολογισμός και εκτίμηση στρεβλών μέτρων κινδύνων με εφαρμογές στον αναλογισμό

Πλατή, Αναστασία

Master Thesis

Author

Πλατή, Αναστασία

Date

2025-09

Abstract

Risk constitutes a fundamental parameter in actuarial science. The need for quantification and effective management has led to the development of various measures aimed at forecasting and assessing potential extreme losses. In this context, the present thesis, based on the scientific approaches of Hardy (2006) and Upretee & Brazauskas (2023), focuses on the theoretical foundation, computation and estimation of an important class of risk measures, known as distortion risk measures. At the same time, their applications in actuarial practice are studied, as well as the approximation methods required when analytical solutions are not feasible. In the first chapter, the fundamental actuarial risk measures are introduced, with emphasis on Value at Risk (VaR) and Conditional Tail Expectation (CTE), along with their comparison. Furthermore, distortion risk measures are presented and the coherence property is examined, as defined by the axioms of Artzner et al. (1999). Finally, alternative risk measures, known as variability measures, such as variance and standard deviation, are discussed, highlighting their limitations in risk assessment. The second chapter investigates the estimation of risk measures through Monte Carlo simulations. The computation of VaR and CTE is analyzed, while both parametric and non-parametric confidence intervals are constructed. In addition, methods for estimating the standard error are presented and the accuracy of the estimators is evaluated, emphasizing the advantages and limitations of this stochastic approach. Finally, the third chapter examines the computation and estimation of distortion risk measures such as Proportional Hazard Transform (PHT), Wang Transform (WT) and Gini Shortfall (GS). Their explicit formulas are presented for selected loss distributions, along with the theoretical bounds that approximate them, which are validated through numerical verification and assessment of estimation quality. Moreover, with the aid of numerical illustrations, the behavior of distributions with similar tail risk is investigated, while Monte Carlo simulations highlight the practical relevance of these measures in cases where the analytical form becomes intractable. Overall, this thesis aims to demonstrate the advantages of distortion risk measures in the assessment of riskiness and to contribute to bridging the gap between theory and practice, thereby enhancing the reliability of risk estimation process in actuarial science.

Postgraduate Studies Programme

Αναλογιστική Επιστήμη και Διαχείριση Κινδύνων

Department

Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

Number of pages

114

Language

Greek

URI

https://dione.lib.unipi.gr/xmlui/handle/unipi/18210

Collections

Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

Show full item record

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