Ruin Probabilities 2nd Edition
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Ruin Probabilities
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Author : S?ren Asmussen
language : en
Publisher: World Scientific
Release Date : 2010
Ruin Probabilities written by S?ren Asmussen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramr?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 2nd Edition
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Author : Soren Asmussen
language : en
Publisher: World Scientific
Release Date : 2010-09-09
Ruin Probabilities 2nd Edition written by Soren Asmussen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-09 with Mathematics categories.
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
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Author : Soren Asmussen
language : en
Publisher: World Scientific
Release Date : 2000-07-24
Ruin Probabilities written by Soren Asmussen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-24 with Mathematics categories.
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.
Introduction To Stochastic Calculus With Applications 2nd Edition
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Author : Fima C Klebaner
language : en
Publisher: World Scientific Publishing Company
Release Date : 2005-06-20
Introduction To Stochastic Calculus With Applications 2nd Edition written by Fima C Klebaner and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-20 with Mathematics categories.
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
Risk Theory A Heavy Tail Approach
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Author : Dimitrios George Konstantinides
language : en
Publisher: #N/A
Release Date : 2017-07-07
Risk Theory A Heavy Tail Approach written by Dimitrios George Konstantinides and has been published by #N/A this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-07 with Mathematics categories.
'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.
Aspects Of Risk Theory
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Author : Jan Grandell
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Aspects Of Risk Theory written by Jan Grandell and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Inhomogeneous Random Evolutions And Their Applications
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Author : Anatoliy Swishchuk
language : en
Publisher: CRC Press
Release Date : 2019-12-11
Inhomogeneous Random Evolutions And Their Applications written by Anatoliy Swishchuk and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-11 with Mathematics categories.
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.
Applied Statistical Methods
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Author : David D. Hanagal
language : en
Publisher: Springer Nature
Release Date : 2022-04-13
Applied Statistical Methods written by David D. Hanagal and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-13 with Mathematics categories.
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.
Stochastic Calculus
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Author : Paolo Baldi
language : en
Publisher: Springer
Release Date : 2017-11-09
Stochastic Calculus written by Paolo Baldi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-09 with Mathematics categories.
This book provides a comprehensive introduction to the theory of stochastic calculus and some of its applications. It is the only textbook on the subject to include more than two hundred exercises with complete solutions. After explaining the basic elements of probability, the author introduces more advanced topics such as Brownian motion, martingales and Markov processes. The core of the book covers stochastic calculus, including stochastic differential equations, the relationship to partial differential equations, numerical methods and simulation, as well as applications of stochastic processes to finance. The final chapter provides detailed solutions to all exercises, in some cases presenting various solution techniques together with a discussion of advantages and drawbacks of the methods used. Stochastic Calculus will be particularly useful to advanced undergraduate and graduate students wishing to acquire a solid understanding of the subject through the theory and exercises. Including full mathematical statements and rigorous proofs, this book is completely self-contained and suitable for lecture courses as well as self-study.
Change Of Time And Change Of Measure Second Edition
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Author : Ole E Barndorff-nielsen
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-05-07
Change Of Time And Change Of Measure Second Edition written by Ole E Barndorff-nielsen and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-07 with Business & Economics categories.
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'.