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Books > Business & Money > Finance > 1584882344
  1. Continuous Stochastic Calculus with Applications to Finance
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  2. Continuous Stochastic Calculus with Applications to Finance

    Delivery: 10-20 Working Days
    Customer Ratings (5 reviews)
    Price R3048.00

Additional Information

The prolonged boom in the US and European stock markets has led to increased interest in the mathematics of security markets, most notably in the theory of stochastic integration. This text gives a rigorous development of the theory of stochastic integration as it applies to the valuation of derivative securities. It includes all the tools necessary for readers to understand how the stochastic integral is constructed with respect to a general continuous martingale.

The author develops the stochastic calculus from first principles, but at a relaxed pace that includes proofs that are detailed, but streamlined to applications to finance. The treatment requires minimal prerequisites-a basic knowledge of measure theoretic probability and Hilbert space theory-and devotes an entire chapter to application in finances, including the Black Scholes market, pricing contingent claims, the general market model, pricing of random payoffs, and interest rate derivatives.

Continuous Stochastic Calculus with Application to Finance is your first opportunity to explore stochastic integration at a reasonable and practical mathematical level. It offers a treatment well balanced between aesthetic appeal, degree of generality, depth, and ease of reading.


Michael Meyer
Brand: Chapman and Hall/CRC
Used Book in Good Condition
Chapman and Hall/CRC
Chapman and Hall/CRC
Chapman and Hall/CRC
Chapman and Hall/CRC
Most Helpful Customer Reviews

Chapter 1: This is a summary of what every probabilist should know about Continuous Time Martingales. Essentially it does, although in a rather terse fashion, and with no examples, for Continuous Time Martingales, what David Williams book, "Probability and Martingales", does for the discreet time case. By restricting himself to the continuous case, as opposed to the more general cadlag processes, the author is able to provide a simple proof of the Doob Meyer Decomposition. The coverage in this chapter is more extensive than that of Chapter 1 in Karatzas and Shreeve and perhaps closer to ChapterII in Rogers and Williams.

Chapter 2: Essentially a brief introduction to Brownian Motion. I would advize the reader to skip this Chapter and replace it with chapter 2 of Karatzas and Shreves "Stochastic Calculus and Brownian Motion". The coverage there is more rigorous.

Chapter 3:This chapter covers Stochatic Integration with respect to a Continous Time Local Martingales... Read more
Time spent to read the book in detail: Four weeks
The book, 295 pages, is ordered as follows:

Chapter 1 (First 50 pages):
These cover discreet time martingale theory.

Expectation/Conditional expectation: The coverage here is unusual and I found it irritating. The author defines conditional expectation of variables in e(P) - the space of extended random variables for which the expectation is defined - i.e. either E(X+) or E(X-) is defined - rather than the more traditional space L^1(R) - the space of integrable random variables. The source of irritation is that the former is not a vector space. Thus given a variable X in e(P) and another variable Y, in general X+Y will not be defined, for example if EX+ = infinity, EY= - infinity. As a result, one is constantly having to worry about whether one can add variables or not, a real pain. Perhaps an example might help:

Suppose I have two variables X1 AND X2. If I am in the space L^1 then I know... Read more
This is a math book first and foremost. It uses advanced mathematical techniques to discuss aspects of randomness that can be used to understand finance. Please don't mistake it for a course to teach concepts in basic finance.

It is a very elegant and sophisticated book for those who are very well versed in the necessary mathematics in stochastic calculus and in particular Martingale theory to show them how these tools can be applied to problems in finance.
If you have the math background and are interested in this topic you will get a lot from this book. If you don't have the math, don't bother. This book will be opaque.
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