The Cramér–Lundberg Model and Its Variants

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Publisher : Springer Nature
ISBN 13 : 3031391055
Total Pages : 252 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis The Cramér–Lundberg Model and Its Variants by : Michel Mandjes

Download or read book The Cramér–Lundberg Model and Its Variants written by Michel Mandjes and published by Springer Nature. This book was released on 2023-12-29 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive examination of the Cramér–Lundberg model, which is the most extensively researched model in ruin theory. It covers the fundamental dynamics of an insurance company's surplus level in great detail, presenting a thorough analysis of the ruin probability and related measures for both the standard model and its variants. Providing a systematic and self-contained approach to evaluate the crucial quantities found in the Cramér–Lundberg model, the book makes use of connections with related queueing models when appropriate, and its emphasis on clean transform-based techniques sets it apart from other works. In addition to consolidating a wealth of existing results, the book also derives several new outcomes using the same methodology. This material is complemented by a thoughtfully chosen collection of exercises. The book's primary target audience is master's and starting PhD students in applied mathematics, operations research, and actuarial science, although it also serves as a useful methodological resource for more advanced researchers. The material is self-contained, requiring only a basic grounding in probability theory and some knowledge of transform techniques.

Stochastic Optimal Control and the U.S. Financial Debt Crisis

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Publisher : Springer Science & Business Media
ISBN 13 : 146143078X
Total Pages : 167 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Stochastic Optimal Control and the U.S. Financial Debt Crisis by : Jerome L. Stein

Download or read book Stochastic Optimal Control and the U.S. Financial Debt Crisis written by Jerome L. Stein and published by Springer Science & Business Media. This book was released on 2012-03-30 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Optimal Control (SOC)—a mathematical theory concerned with minimizing a cost (or maximizing a payout) pertaining to a controlled dynamic process under uncertainty—has proven incredibly helpful to understanding and predicting debt crises and evaluating proposed financial regulation and risk management. Stochastic Optimal Control and the U.S. Financial Debt Crisis analyzes SOC in relation to the 2008 U.S. financial crisis, and offers a detailed framework depicting why such a methodology is best suited for reducing financial risk and addressing key regulatory issues. Topics discussed include the inadequacies of the current approaches underlying financial regulations, the use of SOC to explain debt crises and superiority over existing approaches to regulation, and the domestic and international applications of SOC to financial crises. Principles in this book will appeal to economists, mathematicians, and researchers interested in the U.S. financial debt crisis and optimal risk management.

Level Crossing Methods in Stochastic Models

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Publisher : Springer
ISBN 13 : 3319503324
Total Pages : 574 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Level Crossing Methods in Stochastic Models by : Percy H. Brill

Download or read book Level Crossing Methods in Stochastic Models written by Percy H. Brill and published by Springer. This book was released on 2017-05-04 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a complete update of the first edition of Level Crossing Methods in Stochastic Models, which was published in 2008. Level crossing methods are a set of sample-path based mathematical tools used in applied probability to establish reliable probability distributions. Since the basis for solving any applied probability problem requires a reliable probability distribution, Level Crossing Methods in Stochastic Models, Second Edition is a useful tool for all researchers working on stochastic application problems, including inventory control, queueing theory, reliability theory, actuarial ruin theory, renewal theory, pharmacokinetics, and related Markov processes. The second edition includes a new section with a novel derivation of the Beneš series for M/G/1 queues. It provides new results on the service time for three M/G/I queueing models with bounded workload. It analyzes new applications of queues where zero-wait customers get exceptional service, including several examples on M/G/1 queues, and a new section on G/M/1 queues. Additionally, there are two other important new sections: on the level-crossing derivation of the finite time-t probability distributions of excess, age, and total life, in renewal theory; and on a level-crossing analysis of a risk model in Insurance. The original Chapter 10 has been split into two chapters: the new chapter 10 is on renewal theory, and the first section of the new Chapter 11 is on a risk model. More explicit use is made of the renewal reward theorem throughout, and many technical and editorial changes have been made to facilitate readability. Percy H. Brill, Ph.D., is a Professor emeritus at the University of Windsor, Canada. Dr. Brill is the creator of the level crossing method for analyzing stochastic models. He has published extensively in stochastic processes, queueing theory and related models, especially using level crossing methods.

Introduction to Stochastic Level Crossing Techniques

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Author :
Publisher : CRC Press
ISBN 13 : 1000907376
Total Pages : 394 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Introduction to Stochastic Level Crossing Techniques by : Percy H. Brill

Download or read book Introduction to Stochastic Level Crossing Techniques written by Percy H. Brill and published by CRC Press. This book was released on 2023-07-20 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Stochastic Level Crossing Techniques describes stochastic models and their analysis using the System Point Level Crossing method (abbreviated SPLC or LC). This involves deriving probability density functions (pdfs) or cumulative probability distribution functions (cdfs) of key random variables, applying simple level-crossing limit theorems developed by the author. The pdfs and/or cdfs are used to specify operational characteristics about the stochastic model of interest. The chapters describe distinct stochastic models and associated key random variables in the models. For each model, a figure of a typical sample path (realization, i.e., tracing over time) of the key random variable is displayed. For each model, an analytic (Volterra) integral equation for the stationary pdf of the key random variable is created−by inspection of the sample path, using the simple LC limit theorems. This LC method bypasses a great deal of algebra, usually required by other methods of analysis. The integral equations will be solved directly, or computationally. This book is meant for students of mathematics, management science, engineering, natural sciences, and researchers who use applied probability. It will also be useful to technical workers in a range of professions. Key Features: A description of one representative stochastic model (e.g., a single-server M/G/1 queue; a multiple server M/M/c queue; an inventory system; etc.) Construction of a typical sample path of the key random variable of interest (e.g., the virtual waiting time or workload in queues; the net on-hand inventory in inventory systems; etc.) Statements of the simple LC theorems, which connect the sample-path upcrossing and downcrossing rates across state-space levels, to simple mathematical functions of the stationary pdf of the key random variable, at those state-space levels Creation of (usually Volterra) integral equations for the stationary pdf of the key random variable, by inspection of the sample path Direct analytic solution of the integral equations, where feasible; or, computational solutions of the integral equations Use of the derived stationary pdfs for obtaining operational characteristics of the model

Reinsurance

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Publisher : John Wiley & Sons
ISBN 13 : 0470772689
Total Pages : 366 pages
Book Rating : 4.4/5 (77 download)

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Book Synopsis Reinsurance by : Hansjörg Albrecher

Download or read book Reinsurance written by Hansjörg Albrecher and published by John Wiley & Sons. This book was released on 2017-11-06 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reinsurance: Actuarial and Statistical Aspects provides a survey of both the academic literature in the field as well as challenges appearing in reinsurance practice and puts the two in perspective. The book is written for researchers with an interest in reinsurance problems, for graduate students with a basic knowledge of probability and statistics as well as for reinsurance practitioners. The focus of the book is on modelling together with the statistical challenges that go along with it. The discussed statistical approaches are illustrated alongside six case studies of insurance loss data sets, ranging from MTPL over fire to storm and flood loss data. Some of the presented material also contains new results that have not yet been published in the research literature. An extensive bibliography provides readers with links for further study.

Gerber–Shiu Risk Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 3319023039
Total Pages : 95 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Gerber–Shiu Risk Theory by : Andreas E. Kyprianou

Download or read book Gerber–Shiu Risk Theory written by Andreas E. Kyprianou and published by Springer Science & Business Media. This book was released on 2013-10-02 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by the many and long-standing contributions of H. Gerber and E. Shiu, this book gives a modern perspective on the problem of ruin for the classical Cramér–Lundberg model and the surplus of an insurance company. The book studies martingales and path decompositions, which are the main tools used in analysing the distribution of the time of ruin, the wealth prior to ruin and the deficit at ruin. Recent developments in exotic ruin theory are also considered. In particular, by making dividend or tax payments out of the surplus process, the effect on ruin is explored. Gerber-Shiu Risk Theory can be used as lecture notes and is suitable for a graduate course. Each chapter corresponds to approximately two hours of lectures.

Queues and Lévy Fluctuation Theory

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Publisher : Springer
ISBN 13 : 3319206931
Total Pages : 256 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Queues and Lévy Fluctuation Theory by : Krzysztof Dębicki

Download or read book Queues and Lévy Fluctuation Theory written by Krzysztof Dębicki and published by Springer. This book was released on 2015-08-06 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an extensive introduction to queueing models driven by Lévy-processes as well as a systematic account of the literature on Lévy-driven queues. The objective is to make the reader familiar with the wide set of probabilistic techniques that have been developed over the past decades, including transform-based techniques, martingales, rate-conservation arguments, change-of-measure, importance sampling, and large deviations. On the application side, it demonstrates how Lévy traffic models arise when modelling current queueing-type systems (as communication networks) and includes applications to finance. Queues and Lévy Fluctuation Theory will appeal to postgraduate students and researchers in mathematics, computer science, and electrical engineering. Basic prerequisites are probability theory and stochastic processes.

Number Theory – Diophantine Problems, Uniform Distribution and Applications

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Publisher : Springer
ISBN 13 : 3319553577
Total Pages : 447 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Number Theory – Diophantine Problems, Uniform Distribution and Applications by : Christian Elsholtz

Download or read book Number Theory – Diophantine Problems, Uniform Distribution and Applications written by Christian Elsholtz and published by Springer. This book was released on 2017-05-26 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Robert F. Tichy on the occasion of his 60th birthday. Presenting 22 research and survey papers written by leading experts in their respective fields, it focuses on areas that align with Tichy’s research interests and which he significantly shaped, including Diophantine problems, asymptotic counting, uniform distribution and discrepancy of sequences (in theory and application), dynamical systems, prime numbers, and actuarial mathematics. Offering valuable insights into recent developments in these areas, the book will be of interest to researchers and graduate students engaged in number theory and its applications.

Quasi-Stationary Phenomena in Nonlinearly Perturbed Stochastic Systems

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Author :
Publisher : Walter de Gruyter
ISBN 13 : 3110208253
Total Pages : 593 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Quasi-Stationary Phenomena in Nonlinearly Perturbed Stochastic Systems by : Mats Gyllenberg

Download or read book Quasi-Stationary Phenomena in Nonlinearly Perturbed Stochastic Systems written by Mats Gyllenberg and published by Walter de Gruyter. This book was released on 2008-10-31 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to studies of quasi-stationary phenomena in nonlinearly perturbed stochastic systems. New methods of asymptotic analysis for nonlinearly perturbed stochastic processes based on new types of asymptotic expansions for perturbed renewal equation and recurrence algorithms for construction of asymptotic expansions for Markov type processes with absorption are presented. Asymptotic expansions are given in mixed ergodic (for processes) and large deviation theorems (for absorption times) for nonlinearly perturbed regenerative processes, semi-Markov processes, and Markov chains. Applications to analysis of quasi-stationary phenomena in nonlinearly perturbed queueing systems, population dynamics and epidemic models, and for risk processes are presented. The book also contains an extended bibliography of works in the area. It is an essential reference for theoretical and applied researchers in the field of stochastic processes and their applications and may be also useful for doctoral and advanced undergraduate students.

Mathematical and Statistical Models and Methods in Reliability

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Publisher : Springer Science & Business Media
ISBN 13 : 0817649719
Total Pages : 465 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Mathematical and Statistical Models and Methods in Reliability by : V.V. Rykov

Download or read book Mathematical and Statistical Models and Methods in Reliability written by V.V. Rykov and published by Springer Science & Business Media. This book was released on 2010-11-02 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a selection of invited chapters, all of which deal with various aspects of mathematical and statistical models and methods in reliability. Written by renowned experts in the field of reliability, the contributions cover a wide range of applications, reflecting recent developments in areas such as survival analysis, aging, lifetime data analysis, artificial intelligence, medicine, carcinogenesis studies, nuclear power, financial modeling, aircraft engineering, quality control, and transportation. Mathematical and Statistical Models and Methods in Reliability is an excellent reference text for researchers and practitioners in applied probability and statistics, industrial statistics, engineering, medicine, finance, transportation, the oil and gas industry, and artificial intelligence.

Numerical Modelling of Discrete Materials in Geotechnical Engineering, Civil Engineering and Earth Sciences

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Publisher : CRC Press
ISBN 13 : 9789058096807
Total Pages : 1022 pages
Book Rating : 4.0/5 (968 download)

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Book Synopsis Numerical Modelling of Discrete Materials in Geotechnical Engineering, Civil Engineering and Earth Sciences by : Heinz Konietzky

Download or read book Numerical Modelling of Discrete Materials in Geotechnical Engineering, Civil Engineering and Earth Sciences written by Heinz Konietzky and published by CRC Press. This book was released on 2004-10-15 with total page 1022 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this fully up-to-date volume, important new developments and applications of discrete element modelling are highlighted and brought together for presentation at the First International UDEC/3DEC Symposium. Papers covered the following key areas: * behaviour of masonry structures (walls, bridges, towers, columns) * stability and deformation of tunnels and caverns in fractured rock masses * geomechanical modelling for mining and waste repositories * rock reinforcement design (anchors, shotcrete, bolts) * mechanical and hydro-mechanical behaviour of dams and foundations * rock slope stability, deformation and failure mechanisms * modelling of fundamental rock mechanical problems * modelling of geological processes * constitutive laws for fractured rock masses and masonry structures * dynamic behaviour of discrete structures. Numerical Modelling of Discrete Materials in Geotechnical Engineering, Civil Engineering, and Earth Sciences provides an ultra-modern, in-depth analysis of discrete element modelling in a range of different fields, thus proving valuable reading for civil, mining, and geotechnical engineers, as well as other interested professionals.

Risk and Insurance

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Publisher : Springer Nature
ISBN 13 : 3030351769
Total Pages : 505 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Risk and Insurance by : Søren Asmussen

Download or read book Risk and Insurance written by Søren Asmussen and published by Springer Nature. This book was released on 2020-04-17 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a broad overview of the present state of insurance mathematics and some related topics in risk management, financial mathematics and probability. Both non-life and life aspects are covered. The emphasis is on probability and modeling rather than statistics and practical implementation. Aimed at the graduate level, pointing in part to current research topics, it can potentially replace other textbooks on basic non-life insurance mathematics and advanced risk management methods in non-life insurance. Based on chapters selected according to the particular topics in mind, the book may serve as a source for introductory courses to insurance mathematics for non-specialists, advanced courses for actuarial students, or courses on probabilistic aspects of risk. It will also be useful for practitioners and students/researchers in related areas such as finance and statistics who wish to get an overview of the general area of mathematical modeling and analysis in insurance.

Modern Problems in Insurance Mathematics

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Publisher : Springer
ISBN 13 : 3319066536
Total Pages : 388 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Modern Problems in Insurance Mathematics by : Dmitrii Silvestrov

Download or read book Modern Problems in Insurance Mathematics written by Dmitrii Silvestrov and published by Springer. This book was released on 2014-06-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a compilation of 21 papers presented at the International Cramér Symposium on Insurance Mathematics (ICSIM) held at Stockholm University in June, 2013. The book comprises selected contributions from several large research communities in modern insurance mathematics and its applications. The main topics represented in the book are modern risk theory and its applications, stochastic modelling of insurance business, new mathematical problems in life and non-life insurance and related topics in applied and financial mathematics. The book is an original and useful source of inspiration and essential reference for a broad spectrum of theoretical and applied researchers, research students and experts from the insurance business. In this way, Modern Problems in Insurance Mathematics will contribute to the development of research and academy–industry co-operation in the area of insurance mathematics and its applications.

Ruin Probabilities (2nd Edition)

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Publisher : World Scientific
ISBN 13 : 9814466921
Total Pages : 621 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Ruin Probabilities (2nd Edition) by : Soren Asmussen

Download or read book Ruin Probabilities (2nd Edition) written by Soren Asmussen and published by World Scientific. This book was released on 2010-09-09 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber-Shiu functions and dependence.

Applied Probability and Queues

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Publisher : Springer Science & Business Media
ISBN 13 : 0387215255
Total Pages : 451 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Applied Probability and Queues by : Soeren Asmussen

Download or read book Applied Probability and Queues written by Soeren Asmussen and published by Springer Science & Business Media. This book was released on 2008-01-08 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is a highly recommendable survey of mathematical tools and results in applied probability with special emphasis on queueing theory....The second edition at hand is a thoroughly updated and considerably expended version of the first edition.... This book and the way the various topics are balanced are a welcome addition to the literature. It is an indispensable source of information for both advanced graduate students and researchers." --MATHEMATICAL REVIEWS

Ruin Probabilities

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Author :
Publisher : World Scientific
ISBN 13 : 9810222939
Total Pages : 399 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Ruin Probabilities by : S?ren Asmussen

Download or read book Ruin Probabilities written by S?ren Asmussen and published by World Scientific. This book was released on 2000 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a comprehensive treatment of classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (eg. for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation or periodicity. Special features of the book are the emphasis on change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas like queueing theory.

Mathematical Reviews

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Publisher :
ISBN 13 :
Total Pages : 836 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 1998 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt: