Download or read book Loss Data Analysis written by Henryk Gzyl and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-02-05 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Loss Data Analysis with Maximum Entropy written by Erika Gomes-Gonçalves and published by . This book was released on 2018 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present some results of the application of maximum entropy methods to determine the probability density of compound random variables. This problem is very important in the banking and insurance business, but also appears in system reliability and in operations research. The mathematical tool consists of inverting Laplace transforms of positive compound random variables using the maximum entropy method. This method needs a very small number of (real) values of the Laplace transform, is robust, works with small data sets, and it can be extended to include errors in the data as well as data specified up to intervals. In symbols, the basic typical problem consist in determining the density f S of a compound random variable like S = ∑ Nn=1 X n , or that of a sum of such random variables. There, N is an integer random variable and then X n are a sequence of positive, continuous random variables, independent among themselves and of N. Our methodology can be applied to determine the probability density of the total loss S and that of the individual losses.
Download or read book Maximum Entropy Methods for Loss Data Analysis written by Erika Gomes-Gonçalves and published by . This book was released on 2019 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis of loss data is of utmost interest in many branches of the financial and insurance businesses, in structural engineering and in operations research among others. In the financial industry the determination of the distribution of losses is the first step to take in order to compute regulatory risk capitals, in insurance we need the distribution of losses in order to determine the risk premia. In reliability analysis one needs to determine the distribution of accumulated damage or the first time of occurrence of a composite event, and so on. Not only that, in some cases we have data on the aggregate risk but we happen to be interested in determining the statistical nature of the different types of events that contribute to the aggregate loss.Even though in many of these branches of activity one may have good theoretical descriptions of the underlying processes, the nature of the problems is such that we must resort to numerical methods to actually compute the loss distributions. Besides of being able to determine numerically the distribution of losses, we also need to assess the dependence of the distribution of losses and that of the quantities computed with it, on the empirical data.It is the purpose of this note to illustrate the how the maximum entropy method and its extensions can be used for deal with the various issues that come up in the computation of the distribution of losses.
Download or read book Loss Data Analysis written by Henryk Gzyl and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-03-06 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Loss Data Analysis written by Erika Gomes-Gonçalves and published by . This book was released on 2018 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of determining probability densities from data is important in many fields, in particular in insurance and risk analysis. The method of maximum entropy has proven to be a powerful tool to determine probability densities from a few values of its Laplace transform. This is so, even when the amount of data to compute numerically the Laplace transform is small. But in this case the variability of the reconstruction due to the sample variability in the available data can lead to quite different results. It is the purpose of this note to explore and quantify as much as possible the variability of the densities reconstructed by means of two maxentropic methods: the standard maximum entropy method and its extension to incorporate data with errors. The issues that we consider are of special interest for the advanced measurement approach (AMA) in operational risk, which is based on loss data analysis (LDA) to determine regulatory capital, as well as to determine the loss distribution of risks that occur with low frequency.
Download or read book Maximum Entropy Data Analysis written by Brett Alexander Patterson and published by . This book was released on 1992 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical and Statistical Methods for Actuarial Sciences and Finance written by Marco Corazza and published by Springer. This book was released on 2018-07-17 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interaction between mathematicians, statisticians and econometricians working in actuarial sciences and finance is producing numerous meaningful scientific results. This volume introduces new ideas, in the form of four-page papers, presented at the international conference Mathematical and Statistical Methods for Actuarial Sciences and Finance (MAF), held at Universidad Carlos III de Madrid (Spain), 4th-6th April 2018. The book covers a wide variety of subjects in actuarial science and financial fields, all discussed in the context of the cooperation between the three quantitative approaches. The topics include: actuarial models; analysis of high frequency financial data; behavioural finance; carbon and green finance; credit risk methods and models; dynamic optimization in finance; financial econometrics; forecasting of dynamical actuarial and financial phenomena; fund performance evaluation; insurance portfolio risk analysis; interest rate models; longevity risk; machine learning and soft-computing in finance; management in insurance business; models and methods for financial time series analysis, models for financial derivatives; multivariate techniques for financial markets analysis; optimization in insurance; pricing; probability in actuarial sciences, insurance and finance; real world finance; risk management; solvency analysis; sovereign risk; static and dynamic portfolio selection and management; trading systems. This book is a valuable resource for academics, PhD students, practitioners, professionals and researchers, and is also of interest to other readers with quantitative background knowledge.
Download or read book Software Project Management written by Moh’d A. Radaideh and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-12-18 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Software Project Management (SPM) differs from the Traditional Project Management (PM) approaches in that Software Engineering requires multiple rounds of Software Testing, and Updating in accordance with their Testing results and their customer’s feedback. Thus, SPM introduces unique life cycle processes.This book presents an introduction and a critical analysis of the main Software Project Management Frameworks, and offers the author’s original approach to SPM as developed by him over years of professional and teaching experience in the Academia and the IT/Software Industry. It also provides Executive Summaries of the Project Management and Software Project Management Perspectives offered by the Project Management Institute (PMI), the IEEE-Computer Society (IEEE-CS), and the SCRUM Project Management Bodies such as the SCRUMstudy.
Download or read book Probability Theory written by Werner Linde and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-06-04 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as an introduction to Probability Theory and Mathematical Statistics for students in mathematics, the physical sciences, engineering, and related fields. It is based on the author’s 25 years of experience teaching probability and is squarely aimed at helping students overcome common difficulties in learning the subject. The focus of the book is an explanation of the theory, mainly by the use of many examples. Whenever possible, proofs of stated results are provided. All sections conclude with a short list of problems. The book also includes several optional sections on more advanced topics. This textbook would be ideal for use in a first course in Probability Theory. Contents: Probabilities Conditional Probabilities and Independence Random Variables and Their Distribution Operations on Random Variables Expected Value, Variance, and Covariance Normally Distributed Random Vectors Limit Theorems Introduction to Stochastic Processes Mathematical Statistics Appendix Bibliography Index
Download or read book A Maximum Entropy Approach to the Loss Data Aggregation Problem written by Erika Gomes-Gonçalves and published by . This book was released on 2018 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the main problems in the advanced measurement approach to determine operational risk regulatory capital, consists of the computation of the distribution of losses when the data is made up of aggregated losses caused by different types of risk events in different business lines. A similar problem appears in the insurance industries when there is need of aggregating losses of different types. When the data is well collected, that is, when the losses are collected as a joint vector, the maxentropic techniques are quite suitable for finding the probability density of the aggregated loss. When the data is not well collected, the maxentropic procedure provides us with the marginal densities, which can then be coupled by means of some appropriate copula, and then carry on one of the two procedures that we apply. At any rate, the two possibilities hinge in an essential way on the maxentropic technique to determine a probability density from its Laplace transform. This is due to the fact that such techniques provide us with analytical expressions for the densities, which makes many numerical procedures easier to implement. It is the aim of this note, to examine and compare these alternative ways of solving the problem of determining the density of aggregate losses.
Download or read book Maximum Entropy Data Analysis written by K. Purahoo and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Developments in Maximum Entropy Data Analysis written by David Richard Terence Robinson and published by . This book was released on 1992 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Study of Data Analysis Techniques Involving the Maximum Entropy Method written by Glenn Joseph White and published by . This book was released on 1974 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applications of Maximum Entropy Data Analysis written by McLean Andrew Lister and published by . This book was released on 1995 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Understanding the Digital Transformation of Socio Economic Technological Systems written by Tessaleno Campos Devezas and published by Springer Nature. This book was released on with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computational Intelligence in Decision and Control written by Da Ruan and published by World Scientific. This book was released on 2008 with total page 1201 pages. Available in PDF, EPUB and Kindle. Book excerpt: FLINS, originally an acronym for Fuzzy Logic and Intelligent Technologies in Nuclear Science, is now extended to Computational Intelligence for applied research. The contributions to the eighth edition in the series of FLINS conferences cover state-of-the-art research, development, and technology for computational intelligence systems in general, and for intelligent decision and control in particular.
Download or read book Maximum Entropy and Bayesian Methods Garching Germany 1998 written by Wolfgang von der Linden and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1978 Edwin T. Jaynes and Myron Tribus initiated a series of workshops to exchange ideas and recent developments in technical aspects and applications of Bayesian probability theory. The first workshop was held at the University of Wyoming in 1981 organized by C.R. Smith and W.T. Grandy. Due to its success, the workshop was held annually during the last 18 years. Over the years, the emphasis of the workshop shifted gradually from fundamental concepts of Bayesian probability theory to increasingly realistic and challenging applications. The 18th international workshop on Maximum Entropy and Bayesian Methods was held in Garching / Munich (Germany) (27-31. July 1998). Opening lectures by G. Larry Bretthorst and by Myron Tribus were dedicated to one of th the pioneers of Bayesian probability theory who died on the 30 of April 1998: Edwin Thompson Jaynes. Jaynes revealed and advocated the correct meaning of 'probability' as the state of knowledge rather than a physical property. This inter pretation allowed him to unravel longstanding mysteries and paradoxes. Bayesian probability theory, "the logic of science" - as E.T. Jaynes called it - provides the framework to make the best possible scientific inference given all available exper imental and theoretical information. We gratefully acknowledge the efforts of Tribus and Bretthorst in commemorating the outstanding contributions of E.T. Jaynes to the development of probability theory.
