Generalized Optimal Stopping Problems and Financial Markets (Chapman & Hall/CRC Research Notes in Mathematics Series) [Hardcover]

Dennis Wong (Author)

Book Description

Publication Date: November 7, 1996 | ISBN-10: 0582304008 | ISBN-13: 978-0582304000 | Edition: 1

Provides mathematicians and applied researchers with a well-developed framework in which option pricing can be formulated, and a natural transition from the theory of optimal stopping problems to the valuation of different kinds of options. With the introduction of generalized optimal stopping theory, a unifying approach to option pricing is presented.

Product Details

• Hardcover: 128 pages
• Publisher: Chapman and Hall/CRC; 1 edition (November 7, 1996)
• Language: English
• ISBN-10: 0582304008
• ISBN-13: 978-0582304000
• Product Dimensions: 9.7 x 6.7 x 0.3 inches
• Shipping Weight: 8.3 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #5,764,672 in Books (See Top 100 in Books)

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2 of 2 people found the following review helpful:

5.0 out of 5 stars Well-Written Introduction to Optimal Stopping Theory, March 28, 2006

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Paul Thurston (New York, NY USA) - See all my reviews
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This review is from: Generalized Optimal Stopping Problems and Financial Markets (Chapman & Hall/CRC Research Notes in Mathematics Series) (Hardcover)

The theory of optimal stopping has been a very successful field of study and has numerous applications in quantitative finance. Optimal stopping theory has been used extensively to study American-style options and other contingent claims endowed with early-exercise features.

For a book running a mere 114 pages (include references and bibliography), this reviewer was pleasantly surprised to find such an accessible and careful treatment of the general theory of optimal stopping.

The author keeps the prerequisites to a minimum, but in order to fully appreciate Wong's text, some background material is needed. I recommend Chung's A Course in Probability Theory for the basics in probability & measure theory. For stochastic processes and stochastic calculus, I recommend Rogers & Williams two volume set Diffusions, Markov Processes, and Martingales: Volume 1, Foundations and Diffusions, Markov Processes and Martingales: Volume 2, Itô Calculus. To see how optimal stopping theory is applied in quantitative finance, I recommend Musiela & Rutkowski's Martingale Methods in Financial Modelling.

Wong begins his treatment in Chapter 1 with an overview of the fundamentals of stochastic processes. It is a good idea to read through this chapter as the author sets up the notation used throughout.

Chapter 2 introduces the workhorse of the theory, the Snell Envelope. In order to establish the basic properties of this process, basic concepts such as the essential supremum process & essential supremum measure are studied. The key result established in this chapter is, under suitable conditions, given a process X, the Snell envelope of X is the minimal right-continuous supermartingale dominating X. Regularity conditions (think monotone convergence) are investigated. The chapter wraps up with an investigation of the Davis-Karatzas technique of Lagrange multipliers.

In Chapter 3, the author sets the stage to study financial markets from the point of view of stochastic analysis. This material will be quite familiar to readers of Musiela & Rutkowski.

Chapter 4 provides a review of the contingent claims and introduces European-style and American style options, while

In Chapter 5 the rational prices of American-style options is derived via an application of the properties of the Snell Envelope. The book wraps up in Chapter 6 with a study of options on constrained portfolios, following the work of Cvitanic and Karatzas.

The book contains a good list of references to the published literature. The author didn't include an index; however the table of contents helps the reader find things quickly when using the book as a reference.