Loss Data Analysis

The Maximum Entropy Approach

Henryk Gzyl, Silvia Mayoral, Erika Gomes-Gonçalves

• Publisher: De Gruyter
• Year: 2023
• Print ISBN: 9783111047386
• eBook ISBN: 9783111049700
• Edition: 2
• Topic: Computer Science
• Subtopic: Information Technology
• Index: Computer Science

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

Table of contents

• Title Page
• Copyright
• Contents
• 1 Introduction
• 2 Frequency models
• 3 Individual severity models
• 4 Some detailed examples
• 5 Some traditional approaches to the aggregation problem
• 6 Laplace transforms and fractional moment problems
• 7 The standard maximum entropy method
• 8 Extensions of the method of maximum entropy
• 9 Superresolution in maxentropic Laplace transform inversion
• 10 Sample data dependence
• 11 Disentangling frequencies and decompounding losses
• 12 Computations using the maxentropic density
• 13 A solution to the capital allocation problem
• 14 Review of statistical procedures
• Subject Index