© 2018

Numerical Probability

An Introduction with Applications to Finance


  • 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 Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Gilles Pagès
    Pages 1-26
  3. Gilles Pagès
    Pages 49-94
  4. Gilles Pagès
    Pages 95-132
  5. Gilles Pagès
    Pages 133-173
  6. Gilles Pagès
    Pages 471-507
  7. Gilles Pagès
    Pages 541-562
  8. Back Matter
    Pages 563-579

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.


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

Authors and affiliations

  1. 1.Laboratoire de Probabilités, Statistique et ModélisationSorbonne UniversitéParisFrance

About the authors

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

Industry Sectors
IT & Software
Finance, Business & Banking
Energy, Utilities & Environment
Oil, Gas & Geosciences