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Author: Yasutaka Shimizu Publisher: Springer Nature ISBN: 981169284X Category : Business & Economics Languages : en Pages : 119
Book Description
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: Yasutaka Shimizu Publisher: Springer Nature ISBN: 981169284X Category : Business & Economics Languages : en Pages : 119
Book Description
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 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: O. Hijab Publisher: Springer Science & Business Media ISBN: 1489900136 Category : Science Languages : en Pages : 142
Book Description
The problem of controlling or stabilizing a system of differential equa tions in the presence of random disturbances is intuitively appealing and has been a motivating force behind a wide variety of results grouped loosely together under the heading of "Stochastic Control." This book is concerned with a special instance of this general problem, the "Adaptive LQ Regulator," which is a stochastic control problem of partially observed type that can, in certain cases, be solved explicitly. We first describe this problem, as it is the focal point for the entire book, and then describe the contents of the book. The problem revolves around an uncertain linear system x(O) = x~ in R", where 0 E {1, ... , N} is a random variable representing this uncertainty and (Ai' B , C) and xJ are the coefficient matrices and initial state, respectively, of j j a linear control system, for eachj = 1, ... , N. A common assumption is that the mechanism causing this uncertainty is additive noise, and that conse quently the "controller" has access only to the observation process y( . ) where y = Cex +~.
Author: Harold Kushner Publisher: Springer Science & Business Media ISBN: 9780387952642 Category : Mathematics Languages : en Pages : 12
Book Description
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 ISBN: 3319066536 Category : Business & Economics Languages : en Pages : 388
Book Description
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 ISBN: 1461262925 Category : Business & Economics Languages : en Pages : 436
Book Description
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 ISBN: 1461214823 Category : Mathematics Languages : en Pages : 312
Book Description
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.
Author: Sophia L. Kalpazidou Publisher: Springer Science & Business Media ISBN: 147573929X Category : Mathematics Languages : en Pages : 206
Book Description
This book provides new insight into Markovian dependence via the cycle decompositions. It presents a systematic account of a class of stochastic processes known as cycle (or circuit) processes - so-called because they may be defined by directed cycles. An important application of this approach is the insight it provides to electrical networks and the duality principle of networks. This expanded second edition adds new advances, which reveal wide-ranging interpretations of cycle representations such as homologic decompositions, orthogonality equations, Fourier series, semigroup equations, and disintegration of measures. The text includes chapter summaries as well as a number of detailed illustrations.
Author: Yasutaka Shimizu
Author: Yasutaka Shimizu
Author: Rob Kaas
Author: Subhashis Ghosal
Author: Aleksandr Alekseevich Borovkov
Author: O. Hijab
Author: Harold Kushner
Author: Dmitrii Silvestrov
Author: P. J. Dhrymes
Author: Richard Serfozo
Author: Sophia L. Kalpazidou