Loss Data Analysis: The Maximum Entropy Approach

This is an introductory course on loss data analysis. By that we mean the determination of the density of the probability of cumulative losses. Even though the main motivations come from applications to the insurance, banking and financial industries, the mathematical problem that we shall deal with appears in many application in engineering and natural sciences, where the appropriate name would be accumulated damage data analysis or systems reliability data analysis. Introductory does not mean simple: because the nature of the problems to be treated is complicated, some sophisticated tools may be required to deal with it. To conclude, we mention that all numerical examples were produced using R. 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. - Presents tools for mathematical finance, engineering and the sciences. - Includes real-world mathematical examples and examples developed using R. - This new edition includes a chapter on a numerical approach to solving the capital allocation problem.