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Numerical Probability


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Table of Contents

1 Simulation of random variables.- 2 The Monte Carlo method and applications to option pricing.- 3 Variance reduction.- 4 The Quasi-Monte Carlo method.- 5 Optimal Quantization methods I: cubatures.- 6 Stochastic approximation with applications to finance.- 7 Discretization scheme(s) of a Brownian diffusion.- 8 The diffusion bridge method: application to path-dependent options (II).- 9 Biased Monte Carlo simulation, Multilevel paradigm.- 10 Back to sensitivity computation.- 11 Optimal stopping, Multi-asset American/Bermuda Options.- 12 Miscellany.

About the Author

Gilles Pages is full Professor of Mathematics at Sorbonne Universite (formerly Universite Pierre & Marie Curie) specializing in probability theory, numerical probability and mathematical finance. He was the director of the Laboratoire de Probabiliets & Modeles Aeatoires (now Laboratoire de Probabilites, Statistique et Modelisation) from 2009 to 2014, and has been the director of the Master 2 "Probabilites & 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.

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