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Gzyl, Henryk / Mayoral, Silvia / Gomes-Gonçalves, Erika

Loss Data Analysis

The Maximum Entropy Approach

Series:De Gruyter STEM

    600,00 € / $690.99 / £545.50*

    eBook (EPUB)
    Publication Date:
    February 2018
    ISBN
    978-3-11-051613-5
    See all formats and pricing

    Overview

    • Presents tools for mathematical finance, engineering and the sciences.
    • Includes real-world mathematical examples.

    Aims and Scope

    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

    Details

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    Henryk Gzyl, IESA, Caracas, Venezuela.
    Erika Gomes-Goncalves and Silvia Mayoral, Universidad Carlos III de Madrid, Spain.

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