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Author: Publisher: Springer Science & Business Media ISBN: 3322905705 Category : Technology & Engineering Languages : en Pages : 212
Book Description
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: Publisher: Springer Science & Business Media ISBN: 3322905705 Category : Technology & Engineering Languages : en Pages : 212
Book Description
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 ISBN: 9386279444 Category : Mathematics Languages : en Pages : 212
Book Description
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 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: Andreas Kyprianou Publisher: Springer ISBN: 9783319023045 Category : Mathematics Languages : en Pages : 93
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: R. Beard Publisher: Springer Science & Business Media ISBN: 9401176809 Category : Science Languages : en Pages : 426
Book Description
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: Ariel Rubinstein Publisher: Princeton University Press ISBN: 1400829291 Category : Business & Economics Languages : en Pages : 161
Book Description
Lecture Notes in Microeconomic Theory is the first publication of Ariel Rubinstein's lecture notes from the first part of his well-known course in microeconomic theory, which he has taught for fifteen years to first-year graduate students at Tel Aviv, Princeton, and New York universities. The book will be an invaluable supplement to primary textbooks in microeconomic theory. Conveying the style and method of Rubinstein's lectures, it will benefit teachers and research economists as well as students. The book focuses on and provides a critical assessment of models of rational economic agents, and it contains a large number of original problems. Rubinstein, one of the world's most-respected economics theorists, has made substantial contributions to several fields in economics, particularly game theory. His work is characterized by an unusual combination of deep originality and surprising simplicity. He is probably best known for his contributions to the bargaining problem and, more recently, to bounded rationality.
Author: G.M. Hagen Publisher: Springer Science & Business Media ISBN: 9400963513 Category : Social Science Languages : en Pages : 282
Book Description
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: Nicholas Rescher Publisher: Springer Nature ISBN: 3030785025 Category : Philosophy Languages : en Pages : 83
Book Description
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: Alexander Shapiro Publisher: SIAM ISBN: 0898718759 Category : Mathematics Languages : en Pages : 447
Book Description
Optimization problems involving stochastic models occur in almost all areas of science and engineering, such as telecommunications, medicine, and finance. Their existence compels a need for rigorous ways of formulating, analyzing, and solving such problems. This book focuses on optimization problems involving uncertain parameters and covers the theoretical foundations and recent advances in areas where stochastic models are available. Readers will find coverage of the basic concepts of modeling these problems, including recourse actions and the nonanticipativity principle. The book also includes the theory of two-stage and multistage stochastic programming problems; the current state of the theory on chance (probabilistic) constraints, including the structure of the problems, optimality theory, and duality; and statistical inference in and risk-averse approaches to stochastic programming.
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.
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Author: 
Author: S. Ramasubramanian
Author: Andreas E. Kyprianou
Author: Andreas Kyprianou
Author: R. Beard
Author: Ariel Rubinstein
Author: G.M. Hagen
Author: Nicholas Rescher
Author: Alexander Shapiro
Author: Jan Grandell