Asymptotic Statistics In Insurance Risk Theory
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Author | : Yasutaka Shimizu |
Publisher | : Springer Nature |
Total Pages | : 119 |
Release | : 2022-01-21 |
Genre | : Business & Economics |
ISBN | : 981169284X |
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.
Author | : Rob Kaas |
Publisher | : Springer Science & Business Media |
Total Pages | : 394 |
Release | : 2008-12-03 |
Genre | : Business & Economics |
ISBN | : 3540867368 |
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 | : Subhashis Ghosal |
Publisher | : Cambridge University Press |
Total Pages | : 671 |
Release | : 2017-06-26 |
Genre | : Business & Economics |
ISBN | : 0521878268 |
Bayesian nonparametrics comes of age with this landmark text synthesizing theory, methodology and computation.
Author | : Aleksandr Alekseevich Borovkov |
Publisher | : Cambridge University Press |
Total Pages | : 655 |
Release | : 2008 |
Genre | : Asymptotic expansions |
ISBN | : |
A comprehensive monograph presenting a unified systematic exposition of the large deviations theory for heavy-tailed random walks.
Author | : Dimitrios George Konstantinides |
Publisher | : #N/A |
Total Pages | : 507 |
Release | : 2017-07-07 |
Genre | : Mathematics |
ISBN | : 9813223162 |
'Heavy-tailed risk modelling plays a central role in modern risk theory; within this perspective, the book provides an excellent guide concerning problems and solutions in risk theory.'zbMATHThis 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 | : Ludger Rüschendorf |
Publisher | : Springer Science & Business Media |
Total Pages | : 414 |
Release | : 2013-03-12 |
Genre | : Mathematics |
ISBN | : 364233590X |
The author's particular interest in the area of risk measures is to combine this theory with the analysis of dependence properties. The present volume gives an introduction of basic concepts and methods in mathematical risk analysis, in particular of those parts of risk theory that are of special relevance to finance and insurance. Describing the influence of dependence in multivariate stochastic models on risk vectors is the main focus of the text that presents main ideas and methods as well as their relevance to practical applications. The first part introduces basic probabilistic tools and methods of distributional analysis, and describes their use to the modeling of dependence and to the derivation of risk bounds in these models. In the second, part risk measures with a particular focus on those in the financial and insurance context are presented. The final parts are then devoted to applications relevant to optimal risk allocation, optimal portfolio problems as well as to the optimization of insurance contracts. Good knowledge of basic probability and statistics as well as of basic general mathematics is a prerequisite for comfortably reading and working with the present volume, which is intended for graduate students, practitioners and researchers and can serve as a reference resource for the main concepts and techniques.
Author | : Harold Kushner |
Publisher | : Springer Science & Business Media |
Total Pages | : 12 |
Release | : 2001-06-08 |
Genre | : Mathematics |
ISBN | : 9780387952642 |
One of the first books in the timely and important area of heavy traffic analysis of controlled and uncontrolled stochastics networks, by one of the leading authors in the field. The general theory is developed, with possibly state dependent parameters, and specialized to many different cases of practical interest.
Author | : Dmitrii Silvestrov |
Publisher | : Springer |
Total Pages | : 388 |
Release | : 2014-06-06 |
Genre | : Business & Economics |
ISBN | : 3319066536 |
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.
Author | : P. J. Dhrymes |
Publisher | : Springer Science & Business Media |
Total Pages | : 436 |
Release | : 2012-12-06 |
Genre | : Business & Economics |
ISBN | : 1461262925 |
This book has taken form over several years as a result of a number of courses taught at the University of Pennsylvania and at Columbia University and a series of lectures I have given at the International Monetary Fund. Indeed, I began writing down my notes systematically during the academic year 1972-1973 while at the University of California, Los Angeles. The diverse character of the audience, as well as my own conception of what an introductory and often terminal acquaintance with formal econometrics ought to encompass, have determined the style and content of this volume. The selection of topics and the level of discourse give sufficient variety so that the book can serve as the basis for several types of courses. As an example, a relatively elementary one-semester course can be based on Chapters one through five, omitting the appendices to these chapters and a few sections in some of the chapters so indicated. This would acquaint the student with the basic theory of the general linear model, some of the prob lems often encountered in empirical research, and some proposed solutions. For such a course, I should also recommend a brief excursion into Chapter seven (logit and pro bit analysis) in view of the increasing availability of data sets for which this type of analysis is more suitable than that based on the general linear model.
Author | : Richard Serfozo |
Publisher | : Springer Science & Business Media |
Total Pages | : 312 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461214823 |
Beginning with Jackson networks and ending with spatial queuing systems, this book describes several basic stochastic network processes, with the focus on network processes that have tractable expressions for the equilibrium probability distribution of the numbers of units at the stations. Intended for graduate students and researchers in engineering, science and mathematics interested in the basics of stochastic networks that have been developed over the last twenty years, the text assumes a graduate course in stochastic processes without measure theory, emphasising multi-dimensional Markov processes. Alongside self-contained material on point processes involving real analysis, the book also contains complete introductions to reversible Markov processes, Palm probabilities for stationary systems, Little laws for queuing systems and space-time Poisson processes.