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