Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Ruin Probabilities PDF full book. Access full book title Ruin Probabilities by S?ren Asmussen. Download full books in PDF and EPUB format.
Author: S?ren Asmussen Publisher: World Scientific ISBN: 9814282529 Category : Mathematics Languages : en Pages : 621
Book Description
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.
Author: S?ren Asmussen Publisher: World Scientific ISBN: 9814282529 Category : Mathematics Languages : en Pages : 621
Book Description
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.
Author: Jan Grandell Publisher: Springer Science & Business Media ISBN: 1461390583 Category : Mathematics Languages : en Pages : 186
Book Description
Risk theory, which deals with stochastic models of an insurance business, is a classical application of probability theory. The fundamental problem in risk theory is to investigate the ruin possibility of the risk business. Traditionally the occurrence of the claims is described by a Poisson process and the cost of the claims by a sequence of random variables. This book is a treatise of risk theory with emphasis on models where the occurrence of the claims is described by more general point processes than the Poisson process, such as renewal processes, Cox processes and general stationary point processes. In the Cox case the possibility of risk fluctuation is explicitly taken into account. The presentation is based on modern probabilistic methods rather than on analytic methods. The theory is accompanied with discussions on practical evaluation of ruin probabilities and statistical estimation. Many numerical illustrations of the results are given.
Author: Andreas E. Kyprianou Publisher: Springer Science & Business Media ISBN: 3319023039 Category : Mathematics Languages : en Pages : 95
Book Description
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.
Author: Rob Kaas Publisher: Springer Science & Business Media ISBN: 3540867368 Category : Business & Economics Languages : en Pages : 394
Book Description
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.
Author: Søren Asmussen Publisher: Springer Nature ISBN: 3030351769 Category : Mathematics Languages : en Pages : 505
Book Description
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.
Author: Michel Denuit Publisher: John Wiley & Sons ISBN: 0470016442 Category : Business & Economics Languages : en Pages : 458
Book Description
The increasing complexity of insurance and reinsurance products has seen a growing interest amongst actuaries in the modelling of dependent risks. For efficient risk management, actuaries need to be able to answer fundamental questions such as: Is the correlation structure dangerous? And, if yes, to what extent? Therefore tools to quantify, compare, and model the strength of dependence between different risks are vital. Combining coverage of stochastic order and risk measure theories with the basics of risk management and stochastic dependence, this book provides an essential guide to managing modern financial risk. * Describes how to model risks in incomplete markets, emphasising insurance risks. * Explains how to measure and compare the danger of risks, model their interactions, and measure the strength of their association. * Examines the type of dependence induced by GLM-based credibility models, the bounds on functions of dependent risks, and probabilistic distances between actuarial models. * Detailed presentation of risk measures, stochastic orderings, copula models, dependence concepts and dependence orderings. * Includes numerous exercises allowing a cementing of the concepts by all levels of readers. * Solutions to tasks as well as further examples and exercises can be found on a supporting website. An invaluable reference for both academics and practitioners alike, Actuarial Theory for Dependent Risks will appeal to all those eager to master the up-to-date modelling tools for dependent risks. The inclusion of exercises and practical examples makes the book suitable for advanced courses on risk management in incomplete markets. Traders looking for practical advice on insurance markets will also find much of interest.
Author: Hanspeter Schmidli Publisher: Springer ISBN: 3319720058 Category : Business & Economics Languages : en Pages : 250
Book Description
This book provides an overview of classical actuarial techniques, including material that is not readily accessible elsewhere such as the Ammeter risk model and the Markov-modulated risk model. Other topics covered include utility theory, credibility theory, claims reserving and ruin theory. The author treats both theoretical and practical aspects and also discusses links to Solvency II. Written by one of the leading experts in the field, these lecture notes serve as a valuable introduction to some of the most frequently used methods in non-life insurance. They will be of particular interest to graduate students, researchers and practitioners in insurance, finance and risk management.
Author: Hans Bühlmann Publisher: Springer Science & Business Media ISBN: 3540307117 Category : Mathematics Languages : en Pages : 218
Book Description
From the reviews: "The huge literature in risk theory has been carefully selected and supplemented by personal contributions of the author, many of which appear here for the first time. The result is a systematic and very readable book, which takes into account the most recent developments of the field. It will be of great interest to the actuary as well as to the statistician . . ." -- Math. Reviews Vol. 43
Author: Gordon E. Willmot Publisher: Springer ISBN: 3319713620 Category : Business & Economics Languages : en Pages : 228
Book Description
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.
Author: S?ren Asmussen
Author: S?ren Asmussen
Author: Jan Grandell
Author: Roger J. Gray
Author: Andreas E. Kyprianou
Author: Rob Kaas
Author: Søren Asmussen
Author: Michel Denuit
Author: Hanspeter Schmidli
Author: Hans Bühlmann
Author: Gordon E. Willmot