Gerber Shiu Function In Threshold Insurance Risk Models

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Gerber–Shiu Risk Theory

Author : Andreas E. Kyprianou
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.

Surplus Analysis of Sparre Andersen Insurance Risk Processes

Author : Gordon E. Willmot
Publisher : Springer
ISBN 13 : 3319713620
Total Pages : 228 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Surplus Analysis of Sparre Andersen Insurance Risk Processes by : Gordon E. Willmot

Download or read book Surplus Analysis of Sparre Andersen Insurance Risk Processes written by Gordon E. Willmot and published by Springer. This book was released on 2017-12-21 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This carefully written monograph covers the Sparre Andersen process in an actuarial context using the renewal process as the model for claim counts. A unified reference on Sparre Andersen (renewal risk) processes is included, often missing from existing literature. The authors explore recent results and analyse various risk theoretic quantities associated with the event of ruin, including the time of ruin and the deficit of ruin. Particular attention is given to the explicit identification of defective renewal equation components, which are needed to analyse various risk theoretic quantities and are also relevant in other subject areas of applied probability such as dams and storage processes, as well as queuing theory. Aimed at researchers interested in risk/ruin theory and related areas, this work will also appeal to graduate students in classical and modern risk theory and Gerber-Shiu analysis.

Encyclopedia of Quantitative Risk Analysis and Assessment

Author :
Publisher : John Wiley & Sons
ISBN 13 : 0470035498
Total Pages : 2163 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Encyclopedia of Quantitative Risk Analysis and Assessment by :

Download or read book Encyclopedia of Quantitative Risk Analysis and Assessment written by and published by John Wiley & Sons. This book was released on 2008-09-02 with total page 2163 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leading the way in this field, the Encyclopedia of Quantitative Risk Analysis and Assessment is the first publication to offer a modern, comprehensive and in-depth resource to the huge variety of disciplines involved. A truly international work, its coverage ranges across risk issues pertinent to life scientists, engineers, policy makers, healthcare professionals, the finance industry, the military and practising statisticians. Drawing on the expertise of world-renowned authors and editors in this field this title provides up-to-date material on drug safety, investment theory, public policy applications, transportation safety, public perception of risk, epidemiological risk, national defence and security, critical infrastructure, and program management. This major publication is easily accessible for all those involved in the field of risk assessment and analysis. For ease-of-use it is available in print and online.

Asymptotic Statistics in Insurance Risk Theory

Author : Yasutaka Shimizu
Publisher : Springer Nature
ISBN 13 : 981169284X
Total Pages : 119 pages
Book Rating : 4.8/5 (116 download)

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Book Synopsis Asymptotic Statistics in Insurance Risk Theory by : Yasutaka Shimizu

Download or read book Asymptotic Statistics in Insurance Risk Theory written by Yasutaka Shimizu and published by Springer Nature. This book was released on 2022-01-21 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book begins with the fundamental large sample theory, estimating ruin probability, and ends by dealing with the latest issues of estimating the Gerber–Shiu function. This book is the first to introduce the recent development of statistical methodologies in risk theory (ruin theory) as well as their mathematical validities. Asymptotic theory of parametric and nonparametric inference for the ruin-related quantities is discussed under the setting of not only classical compound Poisson risk processes (Cramér–Lundberg model) but also more general Lévy insurance risk processes. The recent development of risk theory can deal with many kinds of ruin-related quantities: the probability of ruin as well as Gerber–Shiu’s discounted penalty function, both of which are useful in insurance risk management and in financial credit risk analysis. In those areas, the common stochastic models are used in the context of the structural approach of companies’ default. So far, the probabilistic point of view has been the main concern for academic researchers. However, this book emphasizes the statistical point of view because identifying the risk model is always necessary and is crucial in the final step of practical risk management.

Asymptotic Theory in Probability and Statistics with Applications

Author : T. L. Lai
Publisher :
ISBN 13 :
Total Pages : 560 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Asymptotic Theory in Probability and Statistics with Applications by : T. L. Lai

Download or read book Asymptotic Theory in Probability and Statistics with Applications written by T. L. Lai and published by . This book was released on 2008 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a collection of 18 papers, many of which are surveys, on asymptotic theory in probability and statistics, with applications to a variety of problems. This volume comprises three parts: limit theorems, statistics and applications, and mathematical finance and insurance. It is suitable for graduate students in probability and statistics.

Stochastic Processes

Author : Alexander Zeifman
Publisher : MDPI
ISBN 13 : 3039219626
Total Pages : 216 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis Stochastic Processes by : Alexander Zeifman

Download or read book Stochastic Processes written by Alexander Zeifman and published by MDPI. This book was released on 2019-12-12 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this special issue is to publish original research papers that cover recent advances in the theory and application of stochastic processes. There is especial focus on applications of stochastic processes as models of dynamic phenomena in various research areas, such as queuing theory, physics, biology, economics, medicine, reliability theory, and financial mathematics. Potential topics include, but are not limited to: Markov chains and processes; large deviations and limit theorems; random motions; stochastic biological model; reliability, availability, maintenance, inspection; queueing models; queueing network models; computational methods for stochastic models; applications to risk theory, insurance and mathematical finance.

Stochastic Analysis with Financial Applications

Author : Arturo Kohatsu-Higa
Publisher : Springer Science & Business Media
ISBN 13 : 3034800975
Total Pages : 427 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Stochastic Analysis with Financial Applications by : Arturo Kohatsu-Higa

Download or read book Stochastic Analysis with Financial Applications written by Arturo Kohatsu-Higa and published by Springer Science & Business Media. This book was released on 2011-07-22 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic analysis has a variety of applications to biological systems as well as physical and engineering problems, and its applications to finance and insurance have bloomed exponentially in recent times. The goal of this book is to present a broad overview of the range of applications of stochastic analysis and some of its recent theoretical developments. This includes numerical simulation, error analysis, parameter estimation, as well as control and robustness properties for stochastic equations. The book also covers the areas of backward stochastic differential equations via the (non-linear) G-Brownian motion and the case of jump processes. Concerning the applications to finance, many of the articles deal with the valuation and hedging of credit risk in various forms, and include recent results on markets with transaction costs.

Encyclopedia of Quantitative Risk Analysis and Assessment: R-Z

Author : Edward L. Melnick
Publisher :
ISBN 13 :
Total Pages : 616 pages
Book Rating : 4.3/5 ( download)

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Book Synopsis Encyclopedia of Quantitative Risk Analysis and Assessment: R-Z by : Edward L. Melnick

Download or read book Encyclopedia of Quantitative Risk Analysis and Assessment: R-Z written by Edward L. Melnick and published by . This book was released on 2008 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ruin Probabilities

Author : S?ren Asmussen
Publisher : World Scientific
ISBN 13 : 9814282529
Total Pages : 621 pages
Book Rating : 4.8/5 (142 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 2010 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 Cramr?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.

Insurance Risk and Ruin

Author : David C. M. Dickson
Publisher : Cambridge University Press
ISBN 13 : 1316839532
Total Pages : 307 pages
Book Rating : 4.3/5 (168 download)

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Book Synopsis Insurance Risk and Ruin by : David C. M. Dickson

Download or read book Insurance Risk and Ruin written by David C. M. Dickson and published by Cambridge University Press. This book was released on 2016-10-27 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this book is on the two major areas of risk theory: aggregate claims distributions and ruin theory. For aggregate claims distributions, detailed descriptions are given of recursive techniques that can be used in the individual and collective risk models. For the collective model, the book discusses different classes of counting distribution, and presents recursion schemes for probability functions and moments. For the individual model, the book illustrates the three most commonly applied techniques. Beyond the classical topics in ruin theory, this new edition features an expanded section covering time of ruin problems, Gerber–Shiu functions, and the application of De Vylder approximations. Suitable for a first course in insurance risk theory and extensively classroom tested, the book is accessible to readers with a solid understanding of basic probability. Numerous worked examples are included and each chapter concludes with exercises for which complete solutions are provided.

Nonlinear Mathematics for Uncertainty and its Applications

Author : Shoumei Li
Publisher : Springer Science & Business Media
ISBN 13 : 364222833X
Total Pages : 708 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Nonlinear Mathematics for Uncertainty and its Applications by : Shoumei Li

Download or read book Nonlinear Mathematics for Uncertainty and its Applications written by Shoumei Li and published by Springer Science & Business Media. This book was released on 2011-07-21 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of papers presented at the international conference on Nonlinear Mathematics for Uncertainty and Its Applications (NLMUA2011), held at Beijing University of Technology during the week of September 7--9, 2011. The conference brought together leading researchers and practitioners involved with all aspects of nonlinear mathematics for uncertainty and its applications. Over the last fifty years there have been many attempts in extending the theory of classical probability and statistical models to the generalized one which can cope with problems of inference and decision making when the model-related information is scarce, vague, ambiguous, or incomplete. Such attempts include the study of nonadditive measures and their integrals, imprecise probabilities and random sets, and their applications in information sciences, economics, finance, insurance, engineering, and social sciences. The book presents topics including nonadditive measures and nonlinear integrals, Choquet, Sugeno and other types of integrals, possibility theory, Dempster-Shafer theory, random sets, fuzzy random sets and related statistics, set-valued and fuzzy stochastic processes, imprecise probability theory and related statistical models, fuzzy mathematics, nonlinear functional analysis, information theory, mathematical finance and risk managements, decision making under various types of uncertainty, and others.

Risk, Ruin and Survival

Author : Ricardas Zitikis
Publisher : MDPI
ISBN 13 : 3039285165
Total Pages : 210 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis Risk, Ruin and Survival by : Ricardas Zitikis

Download or read book Risk, Ruin and Survival written by Ricardas Zitikis and published by MDPI. This book was released on 2020-04-02 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developing techniques for assessing various risks and calculating probabilities of ruin and survival are exciting topics for mathematically-inclined academics. For practicing actuaries and financial engineers, the resulting insights have provided enormous opportunities but also created serious challenges to overcome, thus facilitating closer cooperation between industries and academic institutions. In this book, several renown researchers with extensive interdisciplinary research experiences share their thoughts that, in one way or another, contribute to the betterment of practice and theory of decision making under uncertainty. Behavioral, cultural, mathematical, and statistical aspects of risk assessment and modelling have been explored, and have been often illustrated using real and simulated data. Topics range from financial and insurance risks to security-type risks, from one-dimensional to multi- and even infinite-dimensional risks. The articles in the book were written with a broad audience in mind and should provide enjoyable reading for those with university level degrees and/or those who have studied for accreditation by various actuarial and financial societies.

Recent Advances in Delay Differential and Difference Equations

Author : Ferenc Hartung
Publisher : Springer
ISBN 13 : 3319082515
Total Pages : 271 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Recent Advances in Delay Differential and Difference Equations by : Ferenc Hartung

Download or read book Recent Advances in Delay Differential and Difference Equations written by Ferenc Hartung and published by Springer. This book was released on 2014-08-22 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Delay differential and difference equations serve as models for a range of processes in biology, physics, engineering and control theory. In this volume, the participants of the International Conference on Delay Differential and Difference Equations and Applications, Balatonfüred, Hungary, July 15-19, 2013 present recent research in this quickly-evolving field. The papers relate to the existence, asymptotic and oscillatory properties of the solutions; stability theory; numerical approximations; and applications to real world phenomena using deterministic and stochastic discrete and continuous dynamical systems.

Modern Problems of Stochastic Analysis and Statistics

Author : Vladimir Panov
Publisher : Springer
ISBN 13 : 331965313X
Total Pages : 506 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Modern Problems of Stochastic Analysis and Statistics by : Vladimir Panov

Download or read book Modern Problems of Stochastic Analysis and Statistics written by Vladimir Panov and published by Springer. This book was released on 2017-11-21 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together the latest findings in the area of stochastic analysis and statistics. The individual chapters cover a wide range of topics from limit theorems, Markov processes, nonparametric methods, acturial science, population dynamics, and many others. The volume is dedicated to Valentin Konakov, head of the International Laboratory of Stochastic Analysis and its Applications on the occasion of his 70th birthday. Contributions were prepared by the participants of the international conference of the international conference “Modern problems of stochastic analysis and statistics”, held at the Higher School of Economics in Moscow from May 29 - June 2, 2016. It offers a valuable reference resource for researchers and graduate students interested in modern stochastics.

The Cramér–Lundberg Model and Its Variants

Author : Michel Mandjes
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.

ASTIN Bulletin

Author :
Publisher :
ISBN 13 :
Total Pages : 568 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis ASTIN Bulletin by :

Download or read book ASTIN Bulletin written by and published by . This book was released on 2007 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Modern Actuarial Risk Theory

Author : Rob Kaas
Publisher : Springer Science & Business Media
ISBN 13 : 3540867368
Total Pages : 394 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Modern Actuarial Risk Theory by : Rob Kaas

Download or read book Modern Actuarial Risk Theory written by Rob Kaas and published by Springer Science & Business Media. This book was released on 2008-12-03 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern Actuarial Risk Theory contains what every actuary needs to know about non-life insurance mathematics. It starts with the standard material like utility theory, individual and collective model and basic ruin theory. Other topics are risk measures and premium principles, bonus-malus systems, ordering of risks and credibility theory. It also contains some chapters about Generalized Linear Models, applied to rating and IBNR problems. As to the level of the mathematics, the book would fit in a bachelors or masters program in quantitative economics or mathematical statistics. This second and.