Approximate Computation of Expectations PDF Download

Author: Charles Stein
Publisher: IMS
ISBN: 9780940600089
Category : Mathematics
Languages : en
Pages : 172

View

Book Description

Author: Doug Huggins
Publisher: John Wiley & Sons
ISBN: 1118477219
Category : Business & Economics
Languages : en
Pages : 389

View

Book Description
As western governments issue increasing amounts of debt, the fixed income markets have never been more important. Yet the methods for analyzing these markets have failed to keep pace with recent developments, including the deterioration in the credit quality of many sovereign issuers. In Fixed Income Relative Value Analysis, Doug Huggins and Christian Schaller address this gap with a set of analytic tools for assessing value in the markets for government bonds, interest rate swaps, and related basis swaps, as well as associated futures and options. Taking a practitioner’s point of view, the book presents the theory behind market analysis in connection with tools for finding and expressing trade ideas. The extensive use of actual market examples illustrates the ways these analytic tools can be applied in practice. The book covers: Statistical models for quantitative market analysis, in particular mean reversion models and principal component analysis. An in-depth approach to understanding swap spreads in theory and in practice. A comprehensive discussion of the various basis swaps and their combinations. The incorporation of credit default swaps in yield curve analysis. A classification of option trades, with appropriate analysis tools for each category. Fitted curve techniques for identifying relative value among different bonds. A multi-factor delivery option model for bond future contracts. Fixed Income Relative Value Analysis provides an insightful presentation of the relevant statistical and financial theories, a detailed set of statistical and financial tools derived from these theories, and a multitude of actual trades resulting from the application of these tools to the fixed income markets. As such, it’s an indispensable guide for relative value analysts, relative value traders, and portfolio managers for whom security selection and hedging are part of the investment process.

Author: Joseph K. Blitzstein
Publisher: CRC Press
ISBN: 1466575573
Category : Mathematics
Languages : en
Pages : 599

View

Book Description
Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.

Author: Michael J. Evans
Publisher: Macmillan
ISBN: 9780716747420
Category : Mathematics
Languages : en
Pages : 704

View

Book Description
Unlike traditional introductory math/stat textbooks, Probability and Statistics: The Science of Uncertainty brings a modern flavor based on incorporating the computer to the course and an integrated approach to inference. From the start the book integrates simulations into its theoretical coverage, and emphasizes the use of computer-powered computation throughout.* Math and science majors with just one year of calculus can use this text and experience a refreshing blend of applications and theory that goes beyond merely mastering the technicalities. They'll get a thorough grounding in probability theory, and go beyond that to the theory of statistical inference and its applications. An integrated approach to inference is presented that includes the frequency approach as well as Bayesian methodology. Bayesian inference is developed as a logical extension of likelihood methods. A separate chapter is devoted to the important topic of model checking and this is applied in the context of the standard applied statistical techniques. Examples of data analyses using real-world data are presented throughout the text. A final chapter introduces a number of the most important stochastic process models using elementary methods. *Note: An appendix in the book contains Minitab code for more involved computations. The code can be used by students as templates for their own calculations. If a software package like Minitab is used with the course then no programming is required by the students.

Author: Paul E. Pfeiffer
Publisher: Elsevier
ISBN: 1483277208
Category : Mathematics
Languages : en
Pages : 420

View

Book Description
Introduction to Applied Probability provides a basis for an intelligent application of probability ideas to a wide variety of phenomena for which it is suitable. It is intended as a tool for learning and seeks to point out and emphasize significant facts and interpretations which are frequently overlooked or confused by the beginner. The book covers more than enough material for a one semester course, enhancing the value of the book as a reference for the student. Notable features of the book are: the systematic handling of combinations of events (Section 3-5); extensive use of the mass concept as an aid to visualization; an unusually careful treatment of conditional probability, independence, and conditional independence (Section 6-4); the resulting clarification facilitates the formulation of many applied problems; the emphasis on events determined by random variables, which gives unity and clarity to many topics important for interpretation; and the utilization of the indicator function, both as a tool for dealing with events and as a notational device in the handling of random variables. Students of mathematics, engineering, biological and physical sciences will find the text highly useful.

Author: Dimitri Bertsekas
Publisher: Athena Scientific
ISBN: 188652923X
Category : Mathematics
Languages : en
Pages : 544

View

Book Description
An intuitive, yet precise introduction to probability theory, stochastic processes, statistical inference, and probabilistic models used in science, engineering, economics, and related fields. This is the currently used textbook for an introductory probability course at the Massachusetts Institute of Technology, attended by a large number of undergraduate and graduate students, and for a leading online class on the subject. The book covers the fundamentals of probability theory (probabilistic models, discrete and continuous random variables, multiple random variables, and limit theorems), which are typically part of a first course on the subject. It also contains a number of more advanced topics, including transforms, sums of random variables, a fairly detailed introduction to Bernoulli, Poisson, and Markov processes, Bayesian inference, and an introduction to classical statistics. The book strikes a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis is explained intuitively in the main text, and then developed in detail (at the level of advanced calculus) in the numerous solved theoretical problems.

Author: Robert M. Gray
Publisher: Cambridge University Press
ISBN: 1139456288
Category : Technology & Engineering
Languages : en
Pages : 479

View

Book Description
This book describes the essential tools and techniques of statistical signal processing. At every stage theoretical ideas are linked to specific applications in communications and signal processing using a range of carefully chosen examples. The book begins with a development of basic probability, random objects, expectation, and second order moment theory followed by a wide variety of examples of the most popular random process models and their basic uses and properties. Specific applications to the analysis of random signals and systems for communicating, estimating, detecting, modulating, and other processing of signals are interspersed throughout the book. Hundreds of homework problems are included and the book is ideal for graduate students of electrical engineering and applied mathematics. It is also a useful reference for researchers in signal processing and communications.

Author: Rick Durrett
Publisher: Cambridge University Press
ISBN: 113949113X
Category : Mathematics
Languages : en
Pages :

View

Book Description
This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.

Author: Scott A. Sisson
Publisher: CRC Press
ISBN: 1351643460
Category : Mathematics
Languages : en
Pages : 513

View

Book Description
As the world becomes increasingly complex, so do the statistical models required to analyse the challenging problems ahead. For the very first time in a single volume, the Handbook of Approximate Bayesian Computation (ABC) presents an extensive overview of the theory, practice and application of ABC methods. These simple, but powerful statistical techniques, take Bayesian statistics beyond the need to specify overly simplified models, to the setting where the model is defined only as a process that generates data. This process can be arbitrarily complex, to the point where standard Bayesian techniques based on working with tractable likelihood functions would not be viable. ABC methods finesse the problem of model complexity within the Bayesian framework by exploiting modern computational power, thereby permitting approximate Bayesian analyses of models that would otherwise be impossible to implement. The Handbook of ABC provides illuminating insight into the world of Bayesian modelling for intractable models for both experts and newcomers alike. It is an essential reference book for anyone interested in learning about and implementing ABC techniques to analyse complex models in the modern world.

Author: John B. Thomas
Publisher: Springer Science & Business Media
ISBN: 1461386586
Category : Technology & Engineering
Languages : en
Pages : 257

View

Book Description
This book was written for an introductory one-term course in probability. It is intended to provide the minimum background in probability that is necessary for students interested in applications to engineering and the sciences. Although it is aimed primarily at upperclassmen and beginning graduate students, the only prere quisite is the standard calculus course usually required of under graduates in engineering and science. Most beginning students will have some intuitive notions of the meaning of probability based on experiences involving, for example, games of chance. This book develops from these notions a set of precise and ordered concepts comprising the elementary theory of probability. An attempt has been made to state theorems carefully, but the level of the proofs varies greatly from formal arguments to appeals to intuition. The book is in no way intended as a substi tu te for a rigorous mathematical treatment of probability. How ever, some small amount of the language of formal mathematics is used, so that the student may become better prepared (at least psychologically) either for more formal courses or for study of the literature. Numerous examples are provided throughout the book. Many of these are of an elementary nature and are intended merely to illustrate textual material. A reasonable number of problems of varying difficulty are provided. Instructors who adopt the text for classroom use may obtain a Solutions Manual for all of the problems by writing to the author.