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Option Pricing and Portfolio Optimization: Modern Methods of Financial Mathematics (Graduate Studies in Mathematics)

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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.