Loss Data Analysis The Maximum Entropy Approach 1st Edition Henryk Gzyl 3110516136 9783110516135

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Product details:

• ISBN 10: 3110516136
• ISBN 13: 9783110516135
• Author: Henryk Gzyl

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.

Table of 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 Review of statistical procedures

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