hal-03907148
https://cnrs.hal.science/hal-03907148
[UNIV-PARIS7] Université Denis Diderot - Paris VII
[CNRS] CNRS - Centre national de la recherche scientifique
[INSMI] CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions
[USPC] Université Sorbonne Paris Cité
[LPSM] Laboratoire de Probabilités, Statistique et Modélisation
[SORBONNE-UNIVERSITE] Sorbonne Université
[SORBONNE-UNIV] Sorbonne Université 01/01/2018
[SU-SCIENCES] Faculté des Sciences de Sorbonne Université
[UNIV-PARIS] Université Paris Cité
[UP-SCIENCES] Université de Paris - Faculté des Sciences
[ALLIANCE-SU] Alliance Sorbonne Université
Numerical Probability
Numerical Probability : An introduction with applications to Finance
Pagès, Gilles
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]
OUV
Monte Carlo method
variance reduction
Quasi-Monte Carlo method
stochastic differential equations
discretization schemes
Euler scheme
Milstein scheme
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 options
least squares regression methods
quantization schemes
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.
2018-08
en
Springer Nature