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This book fulfils its aim of providing good and interesting material for advanced undergraduate study. The Times Higher Education Supplement This is probably one of the best books to begin learning about the sometimes complex topic of stochastic calculus and stochastic processes from a more mathematical approach. Some literature are often accused of unnecessarily complicating the subject when applied to areas of finance. With this book you are allowed to explore the rigorous side of stochastic calculus, yet maintain a physical insight of what is going on. The authors have concentrated on the most important and useful topics that are encountered in common physical and financial systems www.quantnotes.com
Product Description
Stochastic processes are tools used widely by statisticians and researchers working in the mathematics of finance. This book for self-study provides a detailed treatment of conditional expectation and probability, a topic that in principle belongs to probability theory, but is essential as a tool for stochastic processes. The book centers on exercises as the main means of explanation.
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Let be a non-empty set. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
Let be a non-empty set. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Most Helpful Customer Reviews
7 of 7 people found the following review helpful
Format:Paperback
I have extensively used this book for a course on stochastic analysis...The exercises and examples really helped to fully understand the theory. I suggest to read it in conjunction with D. Williams book or Jacod-Protter. The book assumes, anyway, some prerequistes on applied probability, even if the first two chapters are devoted to fix some of these concepts in view of the later chapters.
2 of 2 people found the following review helpful
Format:Paperback
This book is a boon for the non-mathematician financial quant, providing the reader knows some concepts of measure-theoretic probability. The idea of conditional expectation, which is the backbone of the theory of stochastic processes, is developed in considerable detail, which provides an excellent preparation for the study of martingales, Markov chains and Brownian motion in the subsequent chapters. There are numerous exercises scattered all over the chapters with full solutions at chapter ends. Although it does not provide the level of detail that one would get in a book like Oksendal, it certainly reduces the cost of entry into the difficult world of stochastic analysis for the non-mathematician. The only prerequisite is some knowledge of measure-theoretic ideas like Borel sets and Lebesgue measure.
1 of 1 people found the following review helpful
Format:Paperback
Well motivated; well explained; easy to understand! A great read; and still offering readers getting a deeper understanding! There are a number of reasons for this book: An understandable presentation of tools from probability and stochastic processes is especially timely.
With clear explanations, and with lots of examples and illustrations!
A useful first book, before turning to more specialized presentations!
While the subject has a long history and a multitude of applications, there is more recent buzz: It has been suggested that the recent turmoil in financial markets may be caused in part by poor understanding on the part of traders of the mathematical models for derivative trading.
The mathematical tools are widely used, but probably a lot less widely understood!
A bit of history: Stochastic processes is a theory started more than a hundred years ago (1900, Louis Bachlier, a Paris-PhD thesis under Poincare), then Albert Einstein's 1905 discovery of Brownian motion, Norbert Wiener's path-space integral (the 1920ties), K. Ito's integral & formula (the 1940ties) and Paul Samuelson-Merton-Black-Scholes 1974, a stochastic differential equation for option pricing: All mathematical tools devised for the purpose of predicting uncertain outcomes in the world around us: in financial engineering; in physics (quantum mechanics, diffusion & thermodynamics); in biology, and in other parts of our experience.
Review by Palle Jorgensen, March 2010.
With clear explanations, and with lots of examples and illustrations!
A useful first book, before turning to more specialized presentations!
While the subject has a long history and a multitude of applications, there is more recent buzz: It has been suggested that the recent turmoil in financial markets may be caused in part by poor understanding on the part of traders of the mathematical models for derivative trading.
The mathematical tools are widely used, but probably a lot less widely understood!
A bit of history: Stochastic processes is a theory started more than a hundred years ago (1900, Louis Bachlier, a Paris-PhD thesis under Poincare), then Albert Einstein's 1905 discovery of Brownian motion, Norbert Wiener's path-space integral (the 1920ties), K. Ito's integral & formula (the 1940ties) and Paul Samuelson-Merton-Black-Scholes 1974, a stochastic differential equation for option pricing: All mathematical tools devised for the purpose of predicting uncertain outcomes in the world around us: in financial engineering; in physics (quantum mechanics, diffusion & thermodynamics); in biology, and in other parts of our experience.
Review by Palle Jorgensen, March 2010.
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