Mathematical Techniques in Finance: Tools for Incomplete Markets

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Overview

Modern finance overlaps with many fields of mathematics, and for students this can represent considerable strain. Mathematical Techniques in Finance is an ideal textbook for Masters finance courses with a significant quantitative element while also being suitable for finance Ph.D. students. Developed for the highly acclaimed Master of Science in Finance program at Imperial College London, it offers a carefully crafted blend of numerical applications and theoretical grounding in economics, finance, and mathematics. In the best engineering tradition, Ales Cerny mixes tools from calculus, linear algebra, probability theory, numerical mathematics, and programming to analyze in an accessible way some of the most intriguing problems in financial economics. Eighty figures, over 70 worked examples, 25 simple ready-to-run computer programs, and several spreadsheets further enhance the learning experience. Each chapter is followed by a number of classroom-tested exercises with solutions available on the book's web site. Applied mathematics is a craft that requires practice -- this textbook provides plenty of opportunities to practice it and teaches cutting-edge finance into the bargain. Asset pricing is a common theme throughout the book; and readers can follow the development from discrete one-period models to continuous time stochastic processes. This textbook sets itself apart by the comprehensive treatment of pricing and risk measurement in incomplete markets, an area of current research that represents the future in risk management and investment performance evaluation.
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Product Details

  • ISBN-13: 9780691088075
  • Publisher: Princeton University Press
  • Publication date: 11/3/2003
  • Edition description: Older Edition
  • Pages: 352
  • Product dimensions: 5.90 (w) x 9.10 (h) x 1.00 (d)

Meet the Author

Ales Cerny is professor of finance at the Cass Business School, City University London.
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Table of Contents

Preface
1 The Simplest Model of Financial Markets 1
2 Arbitrage and Pricing in the One-Period Model 25
3 Risk and Return in the One-Period Model 55
4 Numerical Techniques for Optimal Portfolio Selection in Incomplete Markets 87
5 Pricing in Dynamically Complete Markets 109
6 Towards Continuous Time 131
7 Fast Fourier Transform 153
8 Information Management 175
9 Martingales and Change of Measure in Finance 193
10 Brownian Motion and Ito Formulae 219
11 Continuous-Time Finance 239
12 Dynamic Option Hedging and Pricing in Incomplete Markets 267
App. A Calculus 313
App. B Probability 337
References 369
Index 373
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