Το σύνθετο λογαριθμοκανονικό-Παρέτο μοντέλο και οι εφαρμογές του στον αναλογισμό

Αγγελοπούλου, Ελευθερία Δήμητρα

Master Thesis

Author

Αγγελοπούλου, Ελευθερία Δήμητρα

Date

2025-09

Abstract

The thesis investigates the properties and applications of the composite lognormal-Pareto model as a response to the need to model data with frequent small losses and rare very large ones. The composite scheme arises from a smooth splice of a lognormal density below a threshold and a Pareto distribution above it, so that the “body” follows a lognormal form and the tail is heavier, yet lighter than that of the classical Pareto distribution. The theoretical background, the baseline model, and its main variants are presented with emphasis on actuarial applications. A brief review of the Pareto and lognormal distributions is provided to justify why the former captures the tail while the latter better fits the body of losses. It is noted that the lognormal underestimates extreme values, whereas the Pareto does not adequately describe small or medium losses, hence the rationale for combining them. The study then presents the model of Cooray & Ananda (2005), Scollnik’s variants (2007), a truncated and re-parameterized scheme [Teodorescu (2010)], and the mixed model of Pigeon & Denuit (2010). Bayesian parameter estimation [Cooray & Cheng (2013)] is also examined. In the empirical section, using the “Danish fire losses” dataset (2,492 losses in millions of Danish kroner, 1980-1990), parameter estimation methods and model comparison criteria are applied, Q-Q plots are examined, and theoretical and empirical quantiles are compared. The results confirm that composite models outperform classical distributions, while among the composite variants some perform better in the body and/or in the tail depending on the criterion. Tables, figures, and implementation details are provided, with the relevant computations and code in the appendix. Finally, broader applications are highlighted in fields where extremes are critical (insurance-financial risk analysis, telecommunications, environment, health), underscoring the usefulness of the lognormal-Pareto model as a flexible tool for heavy-tailed data.

Postgraduate Studies Programme

Αναλογιστική Επιστήμη και Διαχείριση Κινδύνων

Department

Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

Number of pages

106

Language

Greek

URI

https://dione.lib.unipi.gr/xmlui/handle/unipi/18190

Collections

Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

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