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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
Henryk Gzyl
has a PhD in Mathematics from UCSD. He works in Quantitatve Finance and Inverse Problems at The Center for Finance of IESA in Caracas. There he lectures on Risk and Portfolio Optimization.
Silvia Mayoral
is Professor of Finance in the Business Department of Carlos III University, Spain. Her academic activity is devoted to Financial Markets, with a special focus on Risk Measurement and Asset Pricing.
Erika Gomes-Gonçalves
Ph.D. in Business and Quantitative Methods at the University Carlos III of Madrid (UC3M), Spain. Bachelor in Mathematics at Simón Bolívar University (USB), Caracas, Venezuela. Currently, she works as Independent Scholar and Data Science Consultant in Madrid.
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
Henryk Gzyl
has a PhD in Mathematics from UCSD. He works in Quantitatve Finance and Inverse Problems at The Center for Finance of IESA in Caracas. There he lectures on Risk and Portfolio Optimization.
Silvia Mayoral
is Professor of Finance in the Business Department of Carlos III University, Spain. Her academic activity is devoted to Financial Markets, with a special focus on Risk Measurement and Asset Pricing.
Erika Gomes-Gonçalves
Ph.D. in Business and Quantitative Methods at the University Carlos III of Madrid (UC3M), Spain. Bachelor in Mathematics at Simón Bolívar University (USB), Caracas, Venezuela. Currently, she works as Independent Scholar and Data Science Consultant in Madrid.
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