Ruin Probabilities 2nd Edition

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Ruin Probabilities (2nd Edition)

Author : Soren Asmussen
Publisher : World Scientific
ISBN 13 : 9814466921
Total Pages : 621 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Ruin Probabilities (2nd Edition) by : Soren Asmussen

Download or read book Ruin Probabilities (2nd Edition) written by Soren Asmussen and published by World Scientific. This book was released on 2010-09-09 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-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.

Ruin Probabilities

Author : S?ren Asmussen
Publisher : World Scientific
ISBN 13 : 9812779310
Total Pages : 399 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Ruin Probabilities by : S?ren Asmussen

Download or read book Ruin Probabilities written by S?ren Asmussen and published by World Scientific. This book was released on 2000 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text is a treatment of classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramer-Lundberg approximation, exact solutions, other approximations (for example, 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 computational vehicle and the connection to other applied probability areas like queueing theory.

Change Of Time And Change Of Measure (Second Edition)

Author : Ole E Barndorff-nielsen
Publisher : World Scientific Publishing Company
ISBN 13 : 9814678600
Total Pages : 345 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Change Of Time And Change Of Measure (Second Edition) by : Ole E Barndorff-nielsen

Download or read book Change Of Time And Change Of Measure (Second Edition) written by Ole E Barndorff-nielsen and published by World Scientific Publishing Company. This book was released on 2015-05-07 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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'.

Introduction To Stochastic Calculus With Applications (2nd Edition)

Author : Fima C Klebaner
Publisher : World Scientific Publishing Company
ISBN 13 : 1848168225
Total Pages : 431 pages
Book Rating : 4.8/5 (481 download)

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Book Synopsis Introduction To Stochastic Calculus With Applications (2nd Edition) by : Fima C Klebaner

Download or read book Introduction To Stochastic Calculus With Applications (2nd Edition) written by Fima C Klebaner and published by World Scientific Publishing Company. This book was released on 2005-06-20 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author./a

Applied Statistical Methods

Author : David D. Hanagal
Publisher : Springer Nature
ISBN 13 : 9811679320
Total Pages : 318 pages
Book Rating : 4.8/5 (116 download)

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Book Synopsis Applied Statistical Methods by : David D. Hanagal

Download or read book Applied Statistical Methods written by David D. Hanagal and published by Springer Nature. This book was released on 2022-04-13 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects select contributions presented at the International Conference on Importance of Statistics in Global Emerging (ISGES 2020) held at the Department of Mathematics and Statistics, University of Pune, Maharashtra, India, from 2–4 January 2020. It discusses recent developments in several areas of statistics with applications of a wide range of key topics, including small area estimation techniques, Bayesian models for small areas, ranked set sampling, fuzzy supply chain, probabilistic supply chain models, dynamic Gaussian process models, grey relational analysis and multi-item inventory models, and more. The possible use of other models, including generalized Lindley shared frailty models, Benktander Gibrat risk model, decision-consistent randomization method for SMART designs and different reliability models are also discussed. This book includes detailed worked examples and case studies that illustrate the applications of recently developed statistical methods, making it a valuable resource for applied statisticians, students, research project leaders and practitioners from various marginal disciplines and interdisciplinary research.

Inhomogeneous Random Evolutions and Their Applications

Author : Anatoliy Swishchuk
Publisher : CRC Press
ISBN 13 : 0429855052
Total Pages : 253 pages
Book Rating : 4.4/5 (298 download)

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Book Synopsis Inhomogeneous Random Evolutions and Their Applications by : Anatoliy Swishchuk

Download or read book Inhomogeneous Random Evolutions and Their Applications written by Anatoliy Swishchuk and published by CRC Press. This book was released on 2019-12-11 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inhomogeneous Random Evolutions and Their Applications explains how to model various dynamical systems in finance and insurance with non-homogeneous in time characteristics. It includes modeling for: financial underlying and derivatives via Levy processes with time-dependent characteristics; limit order books in the algorithmic and HFT with counting price changes processes having time-dependent intensities; risk processes which count number of claims with time-dependent conditional intensities; multi-asset price impact from distressed selling; regime-switching Levy-driven diffusion-based price dynamics. Initial models for those systems are very complicated, which is why the author’s approach helps to simplified their study. The book uses a very general approach for modeling of those systems via abstract inhomogeneous random evolutions in Banach spaces. To simplify their investigation, it applies the first averaging principle (long-run stability property or law of large numbers [LLN]) to get deterministic function on the long run. To eliminate the rate of convergence in the LLN, it uses secondly the functional central limit theorem (FCLT) such that the associated cumulative process, centered around that deterministic function and suitably scaled in time, may be approximated by an orthogonal martingale measure, in general; and by standard Brownian motion, in particular, if the scale parameter increases. Thus, this approach allows the author to easily link, for example, microscopic activities with macroscopic ones in HFT, connecting the parameters driving the HFT with the daily volatilities. This method also helps to easily calculate ruin and ultimate ruin probabilities for the risk process. All results in the book are new and original, and can be easily implemented in practice.

An Intermediate Course in Probability

Author : Allan Gut
Publisher : Springer Science & Business Media
ISBN 13 : 1441901620
Total Pages : 310 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis An Intermediate Course in Probability by : Allan Gut

Download or read book An Intermediate Course in Probability written by Allan Gut and published by Springer Science & Business Media. This book was released on 2009-06-06 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the only book that gives a rigorous and comprehensive treatment with lots of examples, exercises, remarks on this particular level between the standard first undergraduate course and the first graduate course based on measure theory. There is no competitor to this book. The book can be used in classrooms as well as for self-study.

Risk Theory: A Heavy Tail Approach

Author : Dimitrios George Konstantinides
Publisher : #N/A
ISBN 13 : 9813223162
Total Pages : 507 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Risk Theory: A Heavy Tail Approach by : Dimitrios George Konstantinides

Download or read book Risk Theory: A Heavy Tail Approach written by Dimitrios George Konstantinides and published by #N/A. This book was released on 2017-07-07 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: '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.

Compound Renewal Processes

Author : A. A. Borovkov
Publisher : Cambridge University Press
ISBN 13 : 100911560X
Total Pages : pages
Book Rating : 4.0/5 (91 download)

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Book Synopsis Compound Renewal Processes by : A. A. Borovkov

Download or read book Compound Renewal Processes written by A. A. Borovkov and published by Cambridge University Press. This book was released on 2022-06-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Compound renewal processes (CRPs) are among the most ubiquitous models arising in applications of probability. At the same time, they are a natural generalization of random walks, the most well-studied classical objects in probability theory. This monograph, written for researchers and graduate students, presents the general asymptotic theory and generalizes many well-known results concerning random walks. The book contains the key limit theorems for CRPs, functional limit theorems, integro-local limit theorems, large and moderately large deviation principles for CRPs in the state space and in the space of trajectories, including large deviation principles in boundary crossing problems for CRPs, with an explicit form of the rate functionals, and an extension of the invariance principle for CRPs to the domain of moderately large and small deviations. Applications establish the key limit laws for Markov additive processes, including limit theorems in the domains of normal and large deviations.

Probability

Author : John J. Kinney
Publisher : John Wiley & Sons
ISBN 13 : 111894710X
Total Pages : 480 pages
Book Rating : 4.1/5 (189 download)

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Book Synopsis Probability by : John J. Kinney

Download or read book Probability written by John J. Kinney and published by John Wiley & Sons. This book was released on 2015-01-13 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition "This is a well-written and impressively presented introduction to probability and statistics. The text throughout is highly readable, and the author makes liberal use of graphs and diagrams to clarify the theory." - The Statistician Thoroughly updated, Probability: An Introduction with Statistical Applications, Second Edition features a comprehensive exploration of statistical data analysis as an application of probability. The new edition provides an introduction to statistics with accessible coverage of reliability, acceptance sampling, confidence intervals, hypothesis testing, and simple linear regression. Encouraging readers to develop a deeper intuitive understanding of probability, the author presents illustrative geometrical presentations and arguments without the need for rigorous mathematical proofs. The Second Edition features interesting and practical examples from a variety of engineering and scientific fields, as well as: Over 880 problems at varying degrees of difficulty allowing readers to take on more challenging problems as their skill levels increase Chapter-by-chapter projects that aid in the visualization of probability distributions New coverage of statistical quality control and quality production An appendix dedicated to the use of Mathematica® and a companion website containing the referenced data sets Featuring a practical and real-world approach, this textbook is ideal for a first course in probability for students majoring in statistics, engineering, business, psychology, operations research, and mathematics. Probability: An Introduction with Statistical Applications, Second Edition is also an excellent reference for researchers and professionals in any discipline who need to make decisions based on data as well as readers interested in learning how to accomplish effective decision making from data.

Stochastic Simulation: Algorithms and Analysis

Author : Søren Asmussen
Publisher : Springer Science & Business Media
ISBN 13 : 0387690336
Total Pages : 490 pages
Book Rating : 4.3/5 (876 download)

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Book Synopsis Stochastic Simulation: Algorithms and Analysis by : Søren Asmussen

Download or read book Stochastic Simulation: Algorithms and Analysis written by Søren Asmussen and published by Springer Science & Business Media. This book was released on 2007-07-14 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sampling-based computational methods have become a fundamental part of the numerical toolset of practitioners and researchers across an enormous number of different applied domains and academic disciplines. This book provides a broad treatment of such sampling-based methods, as well as accompanying mathematical analysis of the convergence properties of the methods discussed. The reach of the ideas is illustrated by discussing a wide range of applications and the models that have found wide usage. The first half of the book focuses on general methods; the second half discusses model-specific algorithms. Exercises and illustrations are included.

Probability

Author : Albert Shiryaev
Publisher : Springer Science & Business Media
ISBN 13 : 1475725396
Total Pages : 636 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Probability by : Albert Shiryaev

Download or read book Probability written by Albert Shiryaev and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the Preface to the first edition, originally published in 1980, we mentioned that this book was based on the author's lectures in the Department of Mechanics and Mathematics of the Lomonosov University in Moscow, which were issued, in part, in mimeographed form under the title "Probabil ity, Statistics, and Stochastic Processors, I, II" and published by that Univer sity. Our original intention in writing the first edition of this book was to divide the contents into three parts: probability, mathematical statistics, and theory of stochastic processes, which corresponds to an outline of a three semester course of lectures for university students of mathematics. However, in the course of preparing the book, it turned out to be impossible to realize this intention completely, since a full exposition would have required too much space. In this connection, we stated in the Preface to the first edition that only probability theory and the theory of random processes with discrete time were really adequately presented. Essentially all of the first edition is reproduced in this second edition. Changes and corrections are, as a rule, editorial, taking into account com ments made by both Russian and foreign readers of the Russian original and ofthe English and Germantranslations [Sll]. The author is grateful to all of these readers for their attention, advice, and helpful criticisms. In this second English edition, new material also has been added, as follows: in Chapter 111, §5, §§7-12; in Chapter IV, §5; in Chapter VII, §§8-10.

Asymptotic Statistics in Insurance Risk Theory

Author : Yasutaka Shimizu
Publisher : Springer Nature
ISBN 13 : 981169284X
Total Pages : 119 pages
Book Rating : 4.8/5 (116 download)

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Book Synopsis Asymptotic Statistics in Insurance Risk Theory by : Yasutaka Shimizu

Download or read book Asymptotic Statistics in Insurance Risk Theory written by Yasutaka Shimizu and published by Springer Nature. This book was released on 2022-01-21 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Hedging Derivatives

Author : Thorsten Rheinlander
Publisher : World Scientific
ISBN 13 : 981433880X
Total Pages : 244 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Hedging Derivatives by : Thorsten Rheinlander

Download or read book Hedging Derivatives written by Thorsten Rheinlander and published by World Scientific. This book was released on 2011 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Valuation and hedging of financial derivatives are intrinsically linked concepts. Choosing appropriate hedging techniques depends on both the type of derivative and assumptions placed on the underlying stochastic process. This volume provides a systematic treatment of hedging in incomplete markets. Mean-variance hedging under the risk-neutral measure is applied in the framework of exponential L(r)vy processes and for derivatives written on defaultable assets. It is discussed how to complete markets based upon stochastic volatility models via trading in both stocks and vanilla options. Exponential utility indifference pricing is explored via a duality with entropy minimization. Backward stochastic differential equations offer an alternative approach and are moreover applied to study markets with trading constraints including basis risk. A range of optimal martingale measures are discussed including the entropy, Esscher and minimal martingale measures. Quasi-symmetry properties of stochastic processes are deployed in the semi-static hedging of barrier options. This book is directed towards both graduate students and researchers in mathematical finance, and will also provide an orientation to applied mathematicians, financial economists and practitioners wishing to explore recent progress in this field."

Data Analysis and Related Applications 4

Author : Yiannis Dimotikalis
Publisher : John Wiley & Sons
ISBN 13 : 1394316925
Total Pages : 420 pages
Book Rating : 4.3/5 (943 download)

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Book Synopsis Data Analysis and Related Applications 4 by : Yiannis Dimotikalis

Download or read book Data Analysis and Related Applications 4 written by Yiannis Dimotikalis and published by John Wiley & Sons. This book was released on 2024-09-06 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Probability

Author : Geoffrey Grimmett
Publisher : OUP Oxford
ISBN 13 : 0191019933
Total Pages : 319 pages
Book Rating : 4.1/5 (91 download)

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Book Synopsis Probability by : Geoffrey Grimmett

Download or read book Probability written by Geoffrey Grimmett and published by OUP Oxford. This book was released on 2014-08-21 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains. A special feature is the authors' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford. The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers and the central limit theorem. There is an account of moment generating functions and their applications. The following three chapters are about branching processes, random walks, and continuous-time random processes such as the Poisson process. The final chapter is a fairly extensive account of Markov chains in discrete time. This second edition develops the success of the first edition through an updated presentation, the extensive new chapter on Markov chains, and a number of new sections to ensure comprehensive coverage of the syllabi at major universities.

Fluctuations of Lévy Processes with Applications

Author : Andreas E. Kyprianou
Publisher : Springer Science & Business Media
ISBN 13 : 3642376320
Total Pages : 461 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Fluctuations of Lévy Processes with Applications by : Andreas E. Kyprianou

Download or read book Fluctuations of Lévy Processes with Applications written by Andreas E. Kyprianou and published by Springer Science & Business Media. This book was released on 2014-01-09 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance, continuous-state branching processes and positive self-similar Markov processes. This textbook is based on a series of graduate courses concerning the theory and application of Lévy processes from the perspective of their path fluctuations. Central to the presentation is the decomposition of paths in terms of excursions from the running maximum as well as an understanding of short- and long-term behaviour. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical tractability. The second edition additionally addresses recent developments in the potential analysis of subordinators, Wiener-Hopf theory, the theory of scale functions and their application to ruin theory, as well as including an extensive overview of the classical and modern theory of positive self-similar Markov processes. Each chapter has a comprehensive set of exercises.