Applied Probability and Stochastic Processes Review

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(More customer reviews)I randomly ran across this book in my math library trying to find an extra book to help with the difficult Stochastics Process class I was taking. Little did I know I would find a book I value as much as Douglas Kelly's Introduction to Probability. This book has applied problems and examples! It is not the dry, endless pages of confusing equations we have come to expect from Stochastics Processes books. There is something better out there! This book saved me as an undergraduate, and am now looking forward to it living up to my God like expecations as a post grad. If you are a professor, please use this book for you students. It ties together and lets you appreciate many fields such as linear analysis and even graph theory from computer science. This book will not disappoint.

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This book presents applied probability and stochastic processes in an elementary but mathematically precise manner, with numerous examples and exercises to illustrate the range of engineering and science applications of the concepts. The book is designed to give the reader an intuitive understanding of probabilistic reasoning, in addition to an understanding of mathematical concepts and principles. The initial chapters present a summary of probability and statistics and then Poisson processes, Markov chains, Markov processes and queuing processes are introduced. Advanced topics include simulation, inventory theory, replacement theory, Markov decision theory, and the use of matrix geometric procedures in the analysis of queues.Included in the second edition are appendices at the end of several chapters giving suggestions for the use of Excel in solving the problems of the chapter. Also new in this edition are an introductory chapter on statistics and a chapter on Poisson processes that includes some techniques used in risk assessment. The old chapter on queues has been expanded and broken into two new chapters: one for simple queuing processes and one for queuing networks. Support is provided through the web site http://apsp.tamu.edu where students will have the answers to odd numbered problems and instructors will have access to full solutions and Excel files for homework.

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Financial Modeling Under Non-Gaussian Distributions (Springer Finance) Review

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(More customer reviews)This book is an outstanding a clear presentation of non-Gaussian financial modeling. In financial markets, the Gaussian curve or bell curve, is not accurate in that most markets are skewed (a predisposition to grow on average, not zero) and fat-tailed (rare events such as market crashes happen more often than a Gaussian curve would suggest). Therefore, non-Gaussian modeling is essential to make money in the market or assess risk. This book goes through all the new techniques of non-Gaussian modeling. It does an exceptional job discussing the GARCH generalized autoregressive conditional heteroskedasticity. This is but a fancy word for fluctuations in volatility over time pretty much dependent on recent fluctuations. It works very well I must say empirically, and has tripled the rationality and profitability of my portfolio - especially one of the versions of the GARCH over the others reviewed - but which one I'd rather not say, for obvious reasons ;) The book is weakest at page 183 or so, with the models and I was rather disappointed with the exclusion of the market crash of the 80s in the empirical analysis - wouldn't rare events be the main reason for improving non-Gaussian modeling? Anyway it's rather poor, but thorough, with additive and multivariate GARCHes but the fault lies with the faultiness of the theories not the authors, at least they're encyclopedic. The book picks up at the end with copulas, and a complete discussion of non-Gaussian option pricing. The review of BSM is appreciated and actually well-done, and a nice reminder of what we are trying to improve on exactly. I think this is a most incredible book, very clearly written, and at times, quite an enjoyable read for such a topic. All it takes is multivariate calculus and basic statistics, but more math ability will make the implications and comments breathtaking at times. I often find myself inspired by a passage or footnote to create a whole subroutine in R or python. I think avoiding Bayesian topics and Monte Carlo was disappointing, but wise in terms of focus. A great book for graduate mathematics in applications of statistics or stochastic calculus, or a good book for modeling fundamentals in economics or business management at the post-graduate level.


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This book examines non-Gaussian distributions. It addresses the causes and consequences of non-normality and time dependency in both asset returns and option prices. The book is written for non-mathematicians who want to model financial market prices so the emphasis throughout is on practice. There are abundant empirical illustrations of the models and techniques described, many of which could be equally applied to other financial time series.

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Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling Review

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(More customer reviews)This is the most succinct, clear mathematics book I have ever own. Unlike many mathematics books whose mathematical derivations usually have several missing yet important steps make people scratching their heads, this books is not one of them. All the derivations are very detailed along with great explanations and numerical examples. It is a rare gem in mathematical literature and I salute Prof. Stewart for his great achievement.

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Probability, Markov Chains, Queues, and Simulation provides a modern and authoritative treatment of the mathematical processes that underlie performance modeling. The detailed explanations of mathematical derivations and numerous illustrative examples make this textbook readily accessible to graduate and advanced undergraduate students taking courses in which stochastic processes play a fundamental role. The textbook is relevant to a wide variety of fields, including computer science, engineering, operations research, statistics, and mathematics.

The textbook looks at the fundamentals of probability theory, from the basic concepts of set-based probability, through probability distributions, to bounds, limit theorems, and the laws of large numbers. Discrete and continuous-time Markov chains are analyzed from a theoretical and computational point of view. Topics include the Chapman-Kolmogorov equations; irreducibility; the potential, fundamental, and reachability matrices; random walk problems; reversibility; renewal processes; and the numerical computation of stationary and transient distributions. The M/M/1 queue and its extensions to more general birth-death processes are analyzed in detail, as are queues with phase-type arrival and service processes. The M/G/1 and G/M/1 queues are solved using embedded Markov chains; the busy period, residual service time, and priority scheduling are treated. Open and closed queueing networks are analyzed. The final part of the book addresses the mathematical basis of simulation.

Each chapter of the textbook concludes with an extensive set of exercises. An instructor's solution manual, in which all exercises are completely worked out, is also available (to professors only).

Numerous examples illuminate the mathematical theories
Carefully detailed explanations of mathematical derivations guarantee a valuable pedagogical approach
Each chapter concludes with an extensive set of exercises

Professors: A supplementary Solutions Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: http://press.princeton.edu/class_use/solutions.html

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Modeling and Analysis of Stochastic Systems, Second Edition (Chapman & Hall/CRC Texts in Statistical Science) Review

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(More customer reviews)The book arises from lectures at UNC-CH in a two-semester course on stochastic models. The author has exceptional precision and organization in the classroom, and this comes through in the book. Great book for teachingfrom, as well as learning from. This book also takes a step which more venerable texts, such as the Trivedi book or the Ross series could not -- it has computational excercises suitable for math packages like Mathematica. Thus, the student can be introduced to scientific computer literacy as well as stochastic processes. I recommend this book to anyone interested in teaching today's student, or for preparing themselves for challenges in Operations Research. The book would make an above-average reference as well. Mike Bailey Associate Professor, Naval Postgraduate School

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Based on the author's more than 25 years of teaching experience, Modeling and Analysis of Stochastic Systems, Second Edition covers the most important classes of stochastic processes used in the modeling of diverse systems, from supply chains and inventory systems to genetics and biological systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models. Along with reorganizing the material, this edition revises and adds new exercises and examples.New to the Second EditionA new chapter on diffusion processes that gives an accessible and non-measure-theoretic treatment with applications to financeA more streamlined, application-oriented approach to renewal, regenerative, and Markov regenerative processesTwo appendices that collect relevant results from analysis and differential and difference equationsRather than offer special tricks that work in specific problems, this book provides thorough coverage of general tools that enable the solution and analysis of stochastic models. After mastering the material in the text, students will be well-equipped to build and analyze useful stochastic models for various situations.A collection of MATLAB-based programscan be downloaded from the author's websiteand a solutions manual is available for qualifying instructors.

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Stochastic Modeling: Analysis and Simulation (Dover Books on Mathematics) Review

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(More customer reviews)A good mix of not-too-hard math with practical examples. Good review of probability and statistics. Down-to-earth readable style. My only complaint: A very skimpy index. Overall a great introduction to stochastic processes and their simulation.

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A coherent introduction to the techniques for modeling dynamic stochastic systems, this volume also offers a guide to the mathematical, numerical, and simulation tools of systems analysis. Each chapter opens with an illustrative case study, and comprehensive presentations include formulation of models, determination of parameters, analysis, and interpretation of results. 1995 edition.

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Investment Guarantees: The New Science of Modeling and Risk Management for Equity-Linked Life Insurance Review

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(More customer reviews)As guarantee products are popping up all over the global banking and insurance markets, it is absolutely essential to ensure that the proper financial values are upheld in order to avoid many of the problems that the North American market has faced. 'Investment Guarantees' does a wonderful job of describing these risks in simple enough terms that the pages can be quoted to both financial and non financial people. A very powerful read for those looking to undersand the value of guarantees that are placed on accumulation type insurance products.

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A comprehensive guide to investment guarantees in equity-linked life insuranceDue to the convergence of financial and insurance markets, new forms of investment guarantees are emerging which require financial service professionals to become savvier in modeling and risk management. With chapters that discuss stock return models, dynamic hedging, risk measures, Markov Chain Monte Carlo estimation, and much more, this one-stop reference contains the valuable insights and proven techniques that will allow readers to better understand the theory and practice of investment guarantees and equity-linked insurance policies.Mary Hardy, PhD (Waterloo, Ontario, Canada), is an Associate Professor and Associate Chair of Actuarial Science at the University of Waterloo and is a Fellow of the Institute of Actuaries and an Associate of the Society of Actuaries, where she is a frequent speaker. Her research covers topics in life insurance solvency and risk management, with particular emphasis on equity-linked insurance. Hardy is an Associate Editor of the North American Actuarial Journal and the ASTIN Bulletin and is a Deputy Editor of the British Actuarial Journal.

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