Numerical Probability
An Introduction with Applications to Finance
Authors: Pagès, Gilles
Free Preview- Written by an expert in the subject
- Covers discretization schemes of stochastic differential equations
- Includes over 150 exercises
- Contains an extensive bibliography
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- About this Textbook
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This textbook provides a self-contained introduction to numerical methods in probability with a focus on applications to finance.
Topics covered include the Monte Carlo simulation (including simulation of random variables, variance reduction, quasi-Monte Carlo simulation, and more recent developments such as the multilevel paradigm), stochastic optimization and approximation, discretization schemes of stochastic differential equations, as well as optimal quantization methods. The author further presents detailed applications to numerical aspects of pricing and hedging of financial derivatives, risk measures (such as value-at-risk and conditional value-at-risk), implicitation of parameters, and calibration.
Aimed at graduate students and advanced undergraduate students, this book contains useful examples and over 150 exercises, making it suitable for self-study.
- About the authors
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Gilles Pagès is full Professor of Mathematics at Sorbonne Université (formerly Université Pierre & Marie Curie) specializing in probability theory, numerical probability and mathematical finance. He was the director of the Laboratoire de Probabiliéts & Modèles Aéatoires (now Laboratoire de Probabilités, Statistique et Modélisation) from 2009 to 2014, and has been the director of the Master 2 "Probabilités & Finance", also known as "Master ElKaroui", since 2001. He has published over 100 research articles in probability theory, numerical probability and financial modelling. He is also the author of several graduate and undergraduate textbooks in statistics, applied probability and mathematical finance.
- Table of contents (12 chapters)
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Simulation of Random Variables
Pages 1-26
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The Monte Carlo Method and Applications to Option Pricing
Pages 27-47
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Variance Reduction
Pages 49-94
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The Quasi-Monte Carlo Method
Pages 95-132
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Optimal Quantization Methods I: Cubatures
Pages 133-173
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Table of contents (12 chapters)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Numerical Probability
- Book Subtitle
- An Introduction with Applications to Finance
- Authors
-
- Gilles Pagès
- Series Title
- Universitext
- Copyright
- 2018
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-319-90276-0
- DOI
- 10.1007/978-3-319-90276-0
- Softcover ISBN
- 978-3-319-90274-6
- Series ISSN
- 0172-5939
- Edition Number
- 1
- Number of Pages
- XXI, 579
- Number of Illustrations
- 6 b/w illustrations, 30 illustrations in colour
- Topics
