Overview
- Written by an expert in the subject
- Covers discretization schemes of stochastic differential equations
- Includes over 150 exercises
- Contains an extensive bibliography
Part of the book series: Universitext (UTX)
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
- Monte Carlo method
- variance reduction
- Quasi-Monte Carlo method
- stochastic differential equation discretization schemes
- Euler schemes
- Milstein schemes
- optimal vector quantization
- stochastic approximation
- multilevel extrapolation methods
- Romberg extrapolation methods
- pricing of derivative products
- greeks
- sensitivity computation
- tangent process and log-likelihood method
- Malliavin Monte Carlo
- risk measures
- Value-at-Risk (conditional)
- American option
- least squares regression methods
- quantization schemes
About this book
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.
Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: Numerical Probability
Book Subtitle: An Introduction with Applications to Finance
Authors: Gilles Pagès
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-319-90276-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-319-90274-6Published: 11 August 2018
eBook ISBN: 978-3-319-90276-0Published: 31 July 2018
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XXI, 579
Number of Illustrations: 6 b/w illustrations, 30 illustrations in colour
Topics: Probability Theory and Stochastic Processes, Quantitative Finance, Statistics for Business, Management, Economics, Finance, Insurance