Gzyl / Mayoral / Gomes-Gonçalves Loss Data Analysis

The Maximum Entropy Approach
2. extended Auflage 2023
ISBN: 978-3-11-104970-0
Verlag: De Gruyter
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 222 Seiten

Reihe: De Gruyter STEM

This volume deals with two complementary topics. On one hand the book deals with the problem of determining the the probability distribution of a positive compound random variable, a problem which appears in the banking and insurance industries, in many areas of operational research and in reliability problems in the engineering sciences.

On the other hand, the methodology proposed to solve such problems, which is based on an application of the maximum entropy method to invert the Laplace transform of the distributions, can be applied to many other problems.

The book contains applications to a large variety of problems, including the problem of dependence of the sample data used to estimate empirically the Laplace transform of the random variable.

Contents
Introduction
Frequency models
Individual severity models
Some detailed examples
Some traditional approaches to the aggregation problem
Laplace transforms and fractional moment problems
The standard maximum entropy method
Extensions of the method of maximum entropy
Superresolution in maxentropic Laplace transform inversion
Sample data dependence
Disentangling frequencies and decompounding losses
Computations using the maxentropic density
Review of statistical procedures

Zielgruppe

Professionals and Students in Mathematics, Finance and Insurance.

Autoren/Hrsg.

Gzyl, Henryk

Mayoral, Silvia

Gomes-Gonçalves, Erika

Fachgebiete

• Mathematik | Informatik EDV | Informatik Daten / Datenbanken
• Mathematik | Informatik Mathematik Stochastik

Über Autor(innen)

Henryk Gzyl

has a PhD in Mathematics from UCSD. He works in Quantitatve Finance and Inverse Problems at The Center for Finance of IESA in Caracas. There he lectures on Risk and Portfolio Optimization.

Silvia Mayoral

is Professor of Finance in the Business Department of Carlos III University, Spain. Her academic activity is devoted to Financial Markets, with a special focus on Risk Measurement and Asset Pricing.

Erika Gomes-Gonçalves

Ph.D. in Business and Quantitative Methods at the University Carlos III of Madrid (UC3M), Spain. Bachelor in Mathematics at Simón Bolívar University (USB), Caracas, Venezuela. Currently, she works as Independent Scholar and Data Science Consultant in Madrid.