Lectures On Risk Theory

Author : Anonim
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9783322905703

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Lectures on Risk Theory by Anonim Pdf

Twenty-five years ago, Hans Blihlmann published his famous monograph Mathe matical Methods in Risk Theory in the series Grundlehren der Mathematischen Wis8enschaften and thus established nonlife actuarial mathematics as a recognized subject of probability theory and statistics with a glance towards economics. This book was my guide to the subject when I gave my first course on nonlife actuarial mathematics in Summer 1988, but at the same time I tried to incorporate into my lectures parts of the rapidly growing literature in this area which to a large extent was inspired by Blihlmann's book. The present book is entirely devoted to a single topic of risk theory: Its subject is the development in time of a fixed portfolio of risks. The book thus concentrates on the claim number process and its relatives, the claim arrival process, the aggregate claims process, the risk process, and the reserve process. Particular emphasis is laid on characterizations of various classes of claim number processes, which provide alternative criteria for model selection, and on their relation to the trinity of the binomial, Poisson, and negativebinomial distributions. Special attention is also paid to the mixed Poisson process, which is a useful model in many applications, to the problems of thinning, decomposition, and superposition of risk processe8, which are important with regard to reinsurance, and to the role of martingales, which occur in a natural way in canonical situations.

Author : S. Ramasubramanian
Publisher : Springer
Page : 212 pages
File Size : 40,7 Mb
Release : 2009-04-15
Category : Mathematics
ISBN : 9789386279446

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Lectures on Insurance Models by S. Ramasubramanian Pdf

Insurance has become a necessary aspect of modern society. The mathematical basis of insurance modeling is best expressed in terms of continuous time stochastic processes. This introductory text on actuarial risk theory deals with the Cramer-Lundberg model and the renewal risk model. Their basic structure and properties, including the renewal theorems as well as the corresponding ruin problems, are studied. There is a detailed discussion of heavy tailed distributions, which have become increasingly relevant. The Lundberg risk process with investment in risky asset is also considered. This book will be useful to practitioners in the field and to graduate students interested in this important branch of applied probability.

Author : Andreas E. Kyprianou
Publisher : Springer Science & Business Media
Page : 95 pages
File Size : 50,6 Mb
Release : 2013-10-02
Category : Mathematics
ISBN : 9783319023038

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Gerber–Shiu Risk Theory by Andreas E. Kyprianou Pdf

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 : Andreas Kyprianou
Publisher : Springer
Page : 93 pages
File Size : 52,5 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 3319023047

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Gerber–Shiu Risk Theory by Andreas Kyprianou Pdf

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 : R. Beard
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 47,6 Mb
Release : 2013-04-17
Category : Science
ISBN : 9789401176804

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Risk Theory by R. Beard Pdf

The theory of risk already has its traditions. A review of its classical results is contained in Bohlmann (1909). This classical theory was associated with life insurance mathematics, and dealt mainly with deviations which were expected to be produced by random fluctua tions in individual policies. According to this theory, these deviations are discounted to some initial instant; the square root of the sum of the squares of the capital values calculated in this way then gives a measure for the stability of the portfolio. A theory constituted in this manner is not, however, very appropriate for practical purposes. The fact is that it does not give an answer to such questions as, for example, within what limits a company's probable gain or loss will lie during different periods. Further, non-life insurance, to which risk theory has, in fact, its most rewarding applications, was mainly outside the field of interest of the risk theorists. Thus it is quite understandable that this theory did not receive very much attention and that its applications to practical problems of insurance activity remained rather unimportant. A new phase of development began following the studies of Filip Lundberg (1909, 1919), which, thanks to H. Cramer (1926), e.O.

Author : G.M. Hagen,Fred Wenstøp
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Social Science
ISBN : 9789400963511

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Progress in Utility and Risk Theory by G.M. Hagen,Fred Wenstøp Pdf

1. PROGRESS IN UTILITY AND RISK THEORY At the First International Congress of Utility and Risk Theory in Oslo 1982 (FUR-82) it appeared to be a widespread feeling among the participants that the conference signalled something like a paradigm shift in the field. This does not necessarily mean that old truths were discarded and replaced by new ones, but rather that new theories and new empirical evidence were brought forth, compelling old theories to be critically analyzed from new angels. Some of the papers presented at FUR-82 have been published by Reidel in 1983 in a volume edited by Stigum and Wenst0p. The present volume contains com mentaries on a number of the papers presented at the conference together with broader outlines of current views on the theory. The observation that utility and risk theory now appears to be in a state of rapid change has prompted us to choose the title PROGRESS IN UTILITY AND RISK THEORY for the book, in the belief that science always moves from poorer to more advanced paradigms or from weaker to more forceful theories. In other words, change is usually progress, even though intermediate stages in a para digm shift may be bewildering, to say the least.

Author : Jan Grandell
Publisher : Springer Science & Business Media
Page : 186 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461390589

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Aspects of Risk Theory by Jan Grandell Pdf

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 : Nicholas Rescher
Publisher : Springer Nature
Page : 83 pages
File Size : 44,6 Mb
Release : 2021-10-04
Category : Philosophy
ISBN : 9783030785024

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Risk Theory by Nicholas Rescher Pdf

Apart from its foray into technical issues of risk assessment and management, this book has one principal aim. With situations of chancy outcomes certain key factors—including outcome possibilities, overall expectation, threat, and even luck—are measurable parameters. But risk is something different: it is not measurable a single parametric quantity, but a many-sided factor that has several different components, and constitutes a complex phenomenon that must be assessed judgmentally in a highly contextualized way. This book explains and analyzes how this works out in practice. Topics in this work include choice and risk, chance and likelihood, as well as outcome-yield evaluation and risk. It takes into account abnormal situations and eccentric measurements, situational evaluation and expectation and scrutinizes the social aspect of risk. The book is of interest to logicians, philosophers of mathematics, and researchers of risk assessment. The project is a companion piece to the author's LUCK THEORY, also published by Springer.

Author : Marc Goovaerts,F. Etienne De Vylder,J. Haezendonck
Publisher : Springer Science & Business Media
Page : 477 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9789400946200

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Insurance and Risk Theory by Marc Goovaerts,F. Etienne De Vylder,J. Haezendonck Pdf

Canadian financial institutions have been in rapid change in the past five years. In response to these changes, the Department of Finance issued a discussion paper: The Regulation of Canadian Financial Institutions, in April 1985, and the government intends to introduce legislation in the fall. This paper studi.es the combinantion of financial institutions from the viewpoint of ruin probability. In risk theory developed to describe insurance companies [1,2,3,4,5J, the ruin probability of a company with initial reserve (capital) u is 6 1 -:;-7;;f3 u 1jJ(u) = H6 e H6 (1) Here,we assume that claims arrive as a Poisson process, and the claim amount is distributed as exponential distribution with expectation liS. 6 is the loading, i.e., premium charged is (1+6) times expected claims. Financial institutions are treated as "insurance companies": the difference between interest charged and interest paid is regarded as premiums, loan defaults are treated as claims.

Author : Konstantinides Dimitrios George
Publisher : #N/A
Page : 508 pages
File Size : 46,8 Mb
Release : 2017-07-07
Category : Mathematics
ISBN : 9789813223165

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Risk Theory: A Heavy Tail Approach by Konstantinides Dimitrios George Pdf

This book is written to help graduate students and young researchers to enter quickly into the subject of Risk Theory. It can also be used by actuaries and financial practitioners for the optimization of their decisions and further by regulatory authorities for the stabilization of the insurance industry. The topic of extreme claims is especially presented as a crucial feature of the modern ruin probability.

Author : Hans Bühlmann
Publisher : Unknown
Page : 0 pages
File Size : 40,7 Mb
Release : 1972
Category : Electronic
ISBN : OCLC:1424120771

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Mathematical Methods in Risk Theory by Hans Bühlmann Pdf

Author : Sabine Roeser
Publisher : Springer Science & Business Media
Page : 1209 pages
File Size : 54,9 Mb
Release : 2012
Category : Decision making
ISBN : 9789400714328

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Handbook of Risk Theory by Sabine Roeser Pdf

Risk has become one of the main topics in fields as diverse as engineering, medicine and economics, and it is also studied by social scientists, psychologists and legal scholars. But the topic of risk also leads to more fundamental questions such as: What is risk? What can decision theory contribute to the analysis of risk? What does the human perception of risk mean for society? How should we judge whether a risk is morally acceptable or not? Over the last couple of decades questions like these have attracted interest from philosophers and other scholars into risk theory. This handbook provides for an overview into key topics in a major new field of research. It addresses a wide range of topics, ranging from decision theory, risk perception to ethics and social implications of risk, and it also addresses specific case studies. It aims to promote communication and information among all those who are interested in theoetical issues concerning risk and uncertainty. This handbook brings together internationally leading philosophers and scholars from other disciplines who work on risk theory. The contributions are accessibly written and highly relevant to issues that are studied by risk scholars. We hope that the Handbook of Risk Theory will be a helpful starting point for all risk scholars who are interested in broadening and deepening their current perspectives.

Author : Rafaela Hillerbrand,Per Sandin,Martin Peterson
Publisher : Springer Science & Business Media
Page : 1209 pages
File Size : 47,8 Mb
Release : 2012-01-12
Category : Science
ISBN : 9789400714335

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Handbook of Risk Theory by Rafaela Hillerbrand,Per Sandin,Martin Peterson Pdf

Risk has become one of the main topics in fields as diverse as engineering, medicine and economics, and it is also studied by social scientists, psychologists and legal scholars. But the topic of risk also leads to more fundamental questions such as: What is risk? What can decision theory contribute to the analysis of risk? What does the human perception of risk mean for society? How should we judge whether a risk is morally acceptable or not? Over the last couple of decades questions like these have attracted interest from philosophers and other scholars into risk theory. This handbook provides for an overview into key topics in a major new field of research. It addresses a wide range of topics, ranging from decision theory, risk perception to ethics and social implications of risk, and it also addresses specific case studies. It aims to promote communication and information among all those who are interested in theoetical issues concerning risk and uncertainty. This handbook brings together internationally leading philosophers and scholars from other disciplines who work on risk theory. The contributions are accessibly written and highly relevant to issues that are studied by risk scholars. We hope that the Handbook of Risk Theory will be a helpful starting point for all risk scholars who are interested in broadening and deepening their current perspectives.

Author : Tomasz Rolski,Hanspeter Schmidli,V. Schmidt,Jozef L. Teugels
Publisher : John Wiley & Sons
Page : 680 pages
File Size : 55,5 Mb
Release : 2009-09-25
Category : Mathematics
ISBN : 9780470317884

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Stochastic Processes for Insurance and Finance by Tomasz Rolski,Hanspeter Schmidli,V. Schmidt,Jozef L. Teugels Pdf

Stochastic Processes for Insurance and Finance offers a thorough yet accessible reference for researchers and practitioners of insurance mathematics. Building on recent and rapid developments in applied probability, the authors describe in general terms models based on Markov processes, martingales and various types of point processes. Discussing frequently asked insurance questions, the authors present a coherent overview of the subject and specifically address: The principal concepts from insurance and finance Practical examples with real life data Numerical and algorithmic procedures essential for modern insurance practices Assuming competence in probability calculus, this book will provide a fairly rigorous treatment of insurance risk theory recommended for researchers and students interested in applied probability as well as practitioners of actuarial sciences. Wiley Series in Probability and Statistics

Author : S?ren Asmussen,Hansj”rg Albrecher
Publisher : World Scientific
Page : 621 pages
File Size : 48,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814282529

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Ruin Probabilities by S?ren Asmussen,Hansj”rg Albrecher Pdf

The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cram‚r?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.