Numerical Probability

An Introduction with Applications to Finance

  • Gilles Pagès

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

  • Gilles Pagès
    • 1
  1. 1.Laboratoire de Probabilités, Statistique et ModélisationSorbonne UniversitéParisFrance

Bibliographic information