Option Pricing and Portfolio Optimization: Modern Methods of Financial Mathematics
About this Title
Ralf Korn, University of Kaiserslautern, Germany and Elke Korn, University of Kaiserslautern, Germany. Translated by Ralf Korn, University of Kaiserslautern, Germany
Publication: Graduate Studies in Mathematics
Publication Year 2001: Volume 31
ISBNs: 978-0-8218-2123-7 (print); 978-1-4704-2085-7 (online)
MathSciNet review: MR1802499
MSC: Primary 91-02; Secondary 91B28
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 Itô 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 the 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.
Especially useful for students seeking a lively introduction to Itô calculus.
—Short Book Reviews, International Statistical Institute
Graduate level and research mathematicians, physicists, financial analysts, and actuarians interested in mathematical finance.
Table of Contents
- Chapter 1. The mean-variance approach in a one-period model
- Chapter 2. The continuous-time market model
- Chapter 3. Option pricing
- Chapter 4. Pricing of exotic options and numerical algorithms
- Chapter 5. Optimal portfolios