Change of Time and Change of Measure

Author: Ole E Barndorff-Nielsen
Publisher: World Scientific Publishing Company
ISBN: 9814678600
Format: PDF, Kindle
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Change of Time and Change of Measure provides a comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law. Random change of time is key to understanding the nature of various stochastic processes, and gives rise to interesting mathematical results and insights of importance for the modeling and interpretation of empirically observed dynamic processes. Change of probability law is a technique for solving central questions in mathematical finance, and also has a considerable role in insurance mathematics, large deviation theory, and other fields. The book comprehensively collects and integrates results from a number of scattered sources in the literature and discusses the importance of the results relative to the existing literature, particularly with regard to mathematical finance. In this Second Edition a Chapter 13 entitled 'A Wider View' has been added. This outlines some of the developments that have taken place in the area of Change of Time and Change of Measure since the publication of the First Edition. Most of these developments have their root in the study of the Statistical Theory of Turbulence rather than in Financial Mathematics and Econometrics, and they form part of the new research area termed 'Ambit Stochastics'.

Exercises in Probability

Author: Loïc Chaumont
Publisher: Cambridge University Press
ISBN: 1107606551
Format: PDF, ePub
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Over 100 exercises with detailed solutions, insightful notes and references for further reading. Ideal for beginning researchers.

Ruin Probabilities

Author: Søren Asmussen
Publisher: World Scientific
ISBN: 9814500321
Format: PDF, Docs
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The book is a comprehensive treatment of classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér–Lundberg approximation, exact solutions, other approximations (eg. 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 or periodicity. Special features of the book are the emphasis on change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas like queueing theory. Contents:IntroductionSome General Tools and ResultsThe Compound Poisson ModelThe Probability of Ruin within Finite TimeRenewal ArrivalsRisk Theory in a Markovian EnvironmentPremiums Depending on the Current ReserveMatrix–Analytic MethodsRuin Probabilities in the Presence of Heavy TailsSimulation MethodologyMiscellaneous Topics Readership: Applied mathematicians. keywords:Risk Processes;Ruin Probabilities;Martingales;Random Walks;Markov Additive Processes;Compound Poisson Process;Pollaczeck-Khinchin Formula;Lundberg Conjugation;Laplace Transforms;Diffusion Approximations;Renewal Arrivals;Risk Theory in a Markovian Environment;Heavy Tails;Simulation Methodology;Large Deviations;Reinsurance “This book is a must for anybody working in applied probability. It is a comprehensive treatment of the known results on ruin probabilities…” Short Book Reviews “This is an excellent handbook on the risk theory and brilliant encyclopedia in ruin probabilities results. This book will be useful both for graduate students who deal with stochastic models in insurance mathematics, experts in risk processes and also for those specialists who apply the methods of risk theory in practice.” Zentralblatt Maths “This is a very valuable research monograph, dealing with an area that is mathematically attractive and of considerable relevance to insurance applications. I recommend the book to both experts and beginners in the field.” Mathematical Reviews “No other book covers such a vast area, at least none that is so up-to-date … one can see that Ruin Probabilities is invaluable for researchers in risk theory and perhaps other fields in applied probability. The book can also be used as a textbook for a graduate-level course on ruin theory … The teacher's task is made easy by the recommendation on the introduction on how to get started with the book, and then how to proceed in a second reading.” Journal of the American Statistical Association

Ruin Probabilities

Author: S?ren Asmussen
Publisher: World Scientific
ISBN: 9814282529
Format: PDF, Mobi
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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.

Analysis for Diffusion Processes on Riemannian Manifolds

Author: Feng-Yu Wang
Publisher: World Scientific
ISBN: 9814452653
Format: PDF
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Stochastic analysis on Riemannian manifolds without boundary has been well established. However, the analysis for reflecting diffusion processes and sub-elliptic diffusion processes is far from complete. This book contains recent advances in this direction along with new ideas and efficient arguments, which are crucial for further developments. Many results contained here (for example, the formula of the curvature using derivatives of the semigroup) are new among existing monographs even in the case without boundary.

Local Stereology

Author: Eva B. Vedel Jensen
Publisher: World Scientific
ISBN: 9789810224547
Format: PDF, ePub, Docs
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This book provides a unified exposition of local-stereological methods developed within the last 15 years. The object of local stereology is to draw inference about quantitative parameters of spatial structures which can be regarded as neighbourhoods of points, called reference points. The model example is a biological cell which can be regarded as a neighbourhood of its nucleus. In local stereology, information from sections through the reference point is used. Only very weak assumptions are needed for the structure under study. For instance, specific cell shape assumptions are not necessary.In order to reach a broader audience, the book has been written not only for specialists in stereology, integral geometry and geometric measure theory. In particular, Chapter 1 is an elementary introduction to stereology and the book contains about 75 illustrations. The theory of local steroelogy involves, however, advanced mathematical tools, which constitute an important part of the book.Local-stereological methods are now in world-wide use in the microscopical study of biological tissue, and this invaluable book also contains a description of how the local methods are used in practice.

Elementary Stochastic Calculus with Finance in View

Author: Thomas Mikosch
Publisher: World Scientific
ISBN: 9789810235437
Format: PDF, Mobi
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Modelling with the Ito integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory. This book is suitable for the reader without a deep mathematical background. It gives an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black -- Scholes option pricing formula is derived. The book can serve as a text for a course on stochastic calculus for non-mathematicians or as elementary reading material for anyone who wants to learn about Ito calculus and/or stochastic finance.

Applied Probability and Queues

Author: Soeren Asmussen
Publisher: Springer Science & Business Media
ISBN: 0387215255
Format: PDF, Docs
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"This book is a highly recommendable survey of mathematical tools and results in applied probability with special emphasis on queueing theory....The second edition at hand is a thoroughly updated and considerably expended version of the first edition.... This book and the way the various topics are balanced are a welcome addition to the literature. It is an indispensable source of information for both advanced graduate students and researchers." --MATHEMATICAL REVIEWS

Philosophy of Statistics

Author:
Publisher: Elsevier
ISBN: 9780080930961
Format: PDF, Docs
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Statisticians and philosophers of science have many common interests but restricted communication with each other. This volume aims to remedy these shortcomings. It provides state-of-the-art research in the area of philosophy of statistics by encouraging numerous experts to communicate with one another without feeling “restricted by their disciplines or thinking “piecemeal in their treatment of issues. A second goal of this book is to present work in the field without bias toward any particular statistical paradigm. Broadly speaking, the essays in this Handbook are concerned with problems of induction, statistics and probability. For centuries, foundational problems like induction have been among philosophers’ favorite topics; recently, however, non-philosophers have increasingly taken a keen interest in these issues. This volume accordingly contains papers by both philosophers and non-philosophers, including scholars from nine academic disciplines. Provides a bridge between philosophy and current scientific findings Covers theory and applications Encourages multi-disciplinary dialogue

Statistical Evidence

Author: Richard Royall
Publisher: Routledge
ISBN: 1351414550
Format: PDF, ePub
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Interpreting statistical data as evidence, Statistical Evidence: A Likelihood Paradigm focuses on the law of likelihood, fundamental to solving many of the problems associated with interpreting data in this way. Statistics has long neglected this principle, resulting in a seriously defective methodology. This book redresses the balance, explaining why science has clung to a defective methodology despite its well-known defects. After examining the strengths and weaknesses of the work of Neyman and Pearson and the Fisher paradigm, the author proposes an alternative paradigm which provides, in the law of likelihood, the explicit concept of evidence missing from the other paradigms. At the same time, this new paradigm retains the elements of objective measurement and control of the frequency of misleading results, features which made the old paradigms so important to science. The likelihood paradigm leads to statistical methods that have a compelling rationale and an elegant simplicity, no longer forcing the reader to choose between frequentist and Bayesian statistics.