Books about Stochastic from Amazon.com

Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance. The content of this book has been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The text gives both precise statements of results, plausibility arguments, and even some proofs, but more importantly intuitive explanations developed and refine through classroom experience with this material are provided. The book includes a self-contained treatment of the probability theory needed for stochastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes.

This book is being published in two volumes. This second volume develops stochastic calculus, martingales, risk-neutral pricing, exotic options and term structure models, all in continuous time.

Master's level students and researchers in mathematical finance and financial engineering will find this book useful.

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Price: $48.00 [Notify me when price goes down.]

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Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance. The content of this book has been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The text gives both precise statements of results, plausibility arguments, and even some proofs, but more importantly intuitive explanations developed and refine through classroom experience with this material are provided. The book includes a self-contained treatment of the probability theory needed for stochastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes.

This book is being published in two volumes. The first volume presents the binomial asset-pricing model primarily as a vehicle for introducing in the simple setting the concepts needed for the continuous-time theory in the second volume.

Chapter summaries and detailed illustrations are included. Classroom tested exercises conclude every chapter. Some of these extend the theory and others are drawn from practical problems in quantitative finance.

Advanced undergraduates and Masters level students in mathematical finance and financial engineering will find this book useful.

Steven E. Shreve is Co-Founder of the Carnegie Mellon MS Program in Computational Finance and winner of the Carnegie Mellon Doherty Prize for sustained contributions to education.

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Price: $23.00 [Notify me when price goes down.]

The 2nd edition of this successful book has several new features The calibration discussion of the basic LIBOR market model has been enriched considerably, with an analysis of the impact of the swaptions interpolation technique and of the exogenous instantaneous correlation on the calibration outputs. A discussion of historical estimation of the instantaneous correlation matrix and of rank reduction has been added, and a LIBOR-model consistent swaption-volatility interpolation technique has been introduced.

The old sections devoted to the smile issue in the LIBOR market model have been enlarged into several new chapters. New sections on local-volatility dynamics, and on stochastic volatility models have been added, with a thorough treatment of the recently developed uncertain-volatility approach. Examples of calibrations to real market data are now considered.

The fast-growing interest for hybrid products has led to new chapters. A special focus here is devoted to the pricing of inflation-linked derivatives.

The three final new chapters of this second edition are devoted to credit. Since Credit Derivatives are increasingly fundamental, and since in the reduced-form modeling framework much of the technique involved is analogous to interest-rate modeling, Credit Derivatives -- mostly Credit Default Swaps (CDS), CDS Options and Constant Maturity CDS - are discussed, building on the basic short rate-models and market models introduced earlier for the default-free market. Counterparty risk in interest rate payoff valuation is also considered, motivated by the recent Basel II framework developments.

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Price: $57.64 [Notify me when price goes down.]

This book gives an introduction to the basic theory of stochastic calculus and its applications Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided.

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Price: $30.00 [Notify me when price goes down.]

Monte Carlo simulation has become an essential tool in the pricing of derivative securities and in risk management These applications have, in turn, stimulated research into new Monte Carlo methods and renewed interest in some older techniques.

This book develops the use of Monte Carlo methods in finance and it also uses simulation as a vehicle for presenting models and ideas from financial engineering. It divides roughly into three parts. The first part develops the fundamentals of Monte Carlo methods, the foundations of derivatives pricing, and the implementation of several of the most important models used in financial engineering. The next part describes techniques for improving simulation accuracy and efficiency. The final third of the book addresses special topics: estimating price sensitivities, valuing American options, and measuring market risk and credit risk in financial portfolios.

The most important prerequisite is familiarity with the mathematical tools used to specify and analyze continuous-time models in finance, in particular the key ideas of stochastic calculus. Prior exposure to the basic principles of option pricing is useful but not essential.

The book is aimed at graduate students in financial engineering, researchers in Monte Carlo simulation, and practitioners implementing models in industry.

Mathematical Reviews, 2004: "... this book is very comprehensive, up-to-date and useful tool for those who are interested in implementing Monte Carlo methods in a financial context."

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Price: $47.00 [Notify me when price goes down.]

Todays traders want to know when volatility is a sign that the sky is falling (and they should stay out of the market), and when it is a sign of a possible trading opportunity. Inside Volatility Arbitrage can help them do this. Author and financial expert Alireza Javaheri uses the classic approach to evaluating volatility -- time series and financial econometrics -- in a way that he believes is superior to methods presently used by market participants. He also suggests that there may be "skewness" trading opportunities that can be used to trade the markets more profitably. Filled with in-depth insight and expert advice, Inside Volatility Arbitrage will help traders discover when "skewness" may present valuable trading opportunities as well as why it can be so profitable..
Price: $49.99 [Notify me when price goes down.]

Imagine an equilateral triangle. Now, imagine smaller equilateral triangles perched in the center of each side of the original triangle--you have a Star of David. Now, place still smaller equilateral triangles in the center of each of the star's 12 sides. Repeat this process infinitely and you have a Koch snowflake, a mind-bending geometric figure with an infinitely large perimeter, yet with a finite area. This is an example of the kind of mathematical puzzles that this book addresses.

The Fractal Geometry of Nature is a mathematics text. But buried in the deltas and lambdas and integrals, even a layperson can pick out and appreciate Mandelbrot's point: that somewhere in mathematics, there is an explanation for nature. It is not a coincidence that fractal math is so good at generating images of cliffs and shorelines and capillary beds..
Price: $12.00 [Notify me when price goes down.]

A complete and accessible introduction to the real-world applications of approximate dynamic programming

With the growing levels of sophistication in modern-day operations, it is vital for practitioners to understand how to approach, model, and solve complex industrial problems. Approximate Dynamic Programming is a result of the author's decades of experience working in large industrial settings to develop practical and high-quality solutions to problems that involve making decisions in the presence of uncertainty. This groundbreaking book uniquely integrates four distinct disciplines-Markov design processes, mathematical programming, simulation, and statistics-to demonstrate how to successfully model and solve a wide range of real-life problems using the techniques of approximate dynamic programming (ADP). The reader is introduced to the three curses of dimensionality that impact complex problems and is also shown how the post-decision state variable allows for the use of classical algorithmic strategies from operations research to treat complex stochastic optimization problems.

Designed as an introduction and assuming no prior training in dynamic programming of any form, Approximate Dynamic Programming contains dozens of algorithms that are intended to serve as a starting point in the design of practical solutions for real problems. The book provides detailed coverage of implementation challenges including: modeling complex sequential decision processes under uncertainty, identifying robust policies, designing and estimating value function approximations, choosing effective stepsize rules, and resolving convergence issues.

With a focus on modeling and algorithms in conjunction with the language of mainstream operations research, artificial intelligence, and control theory, Approximate Dynamic Programming:
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Models complex, high-dimensional problems in a natural and practical way, which draws on years of industrial projects
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Introduces and emphasizes the power of estimating a value function around the post-decision state, allowing solution algorithms to be broken down into three fundamental steps: classical simulation, classical optimization, and classical statistics
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Presents a thorough discussion of recursive estimation, including fundamental theory and a number of issues that arise in the development of practical algorithms
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Offers a variety of methods for approximating dynamic programs that have appeared in previous literature, but that have never been presented in the coherent format of a book

Motivated by examples from modern-day operations research, Approximate Dynamic Programming is an accessible introduction to dynamic modeling and is also a valuable guide for the development of high-quality solutions to problems that exist in operations research and engineering. The clear and precise presentation of the material makes this an appropriate text for advanced undergraduate and beginning graduate courses, while also serving as a reference for researchers and practitioners. A companion Web site is available for readers, which includes additional exercises, solutions to exercises, and data sets to reinforce the book's main concepts..
Price: $88.88 [Notify me when price goes down.]

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Price: $14.94 [Notify me when price goes down.]