Option Pricing and Portfolio Optimization: Modern Methods of Financial Mathematics (Graduate Studies in Mathematics) | 
 enlarge | Authors: Ralf Korn, Elke Korn
Publisher: American Mathematical Society
Category: Book
List Price: $41.00
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Rating:  1 reviews
Sales Rank: 1098275
Media: Hardcover
Pages: 253
Number Of Items: 1
Shipping Weight (lbs): 1.5
Dimensions (in): 10.2 x 6.9 x 0.8
ISBN: 0821821237
Dewey Decimal Number: 332.63228
EAN: 9780821821237
Publication Date: January 2001
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Product Description
Understanding and working with the current models of financial markets requires a sound knowledge of the mathematical tools and ideas from which they are built. Banks and financial houses all over the world recognize this and are avidly recruiting mathematicians, physicists, and other scientists with these skills. The mathematics involved in modern finance springs from the heart of probability and analysis: the Ito calculus, stochastic control, differential equations, martingales, and so on. The authors give rigorous treatments of these topics, while always keeping the applications in mind. Thus, the way in which the mathematics is developed is governed by the way it will be used, rather than by the goal of optimal generality.Indeed, most of purely mathematical topics are treated in extended 'excursions' from the applications into the theory. Thus, with the main topic of financial modelling and optimization in view, the reader also obtains a self-contained and complete introduction to the underlying mathematics. This book is specifically designed as a graduate textbook. It could be used for the second part of a course in probability theory, as it includes an applied introduction to the basics of stochastic processes (martingales and Brownian motion) and stochastic calculus. It would also be suitable for a course in continuous-time finance that assumes familiarity with stochastic processes. The prerequisites are basic probability theory and calculus. Some background in stochastic processes would be useful, but not essential.
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| Customer Reviews:
Introduction to Financial Mathematics April 2, 2008
Palle E T Jorgensen (Iowa City, Iowa United States)
In the past few years, introductory courses to Financial Mathematics have become more common. They offer an excellent opportunity for math departments to revitalize their interdisciplinary course offerings. For the students this is a window into a "new world," or a new set of opportunities. This book serves the purpose well.
It is designed for beginning graduate students or advanced undergrads. It offers the right mix of pure and applied. In particular, the authors are familiar with the practical side of the subject; and the appropriate theories from mathematical probability, stochastic integrals, stochastic processed are presented in a logical fashion: advancing logically in steps, good mix of exercises, user-friendly.
The subject of financial mathematics includes option pricing and portfolio optimization, stochastic integration, rigorous methods due to Ito and Feynman-Kac, Monte-Carlo simulation, among others.
The prerequisite include a little measure theory, differential equations, and functional analysis.
With Newton's calculus we solve dynamical equations, integral equations are used in the standard approach to ODE and PDE: Deterministic! Contrast: Ito's lemma! A new feature in stochastic integration (that sets it apart as a subject) is that it addresses mathematical tools needed for dealing with uncertainty in predictions! Review by Palle Jorgensen; April 2008.
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