HAL CCSD
Numerical Probability
Numerical Probability: An introduction with applications to Finance
Pagès, Gilles
Laboratoire de Probabilités, Statistique et Modélisation (LPSM (UMR_8001)) ; Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)
Autres éditeurs de la collection : Carles Casacuberta, Angus MacIntyre, Kenneth Ribet, Claude Sabbah, Endre Süli,Wojbor A. Woyczyński
International audience
ISBN: 978-3-319-90274-6
Ed. Sheldon Axler et al.
Springer Nature
hal-03907148
https://cnrs.hal.science/hal-03907148
https://cnrs.hal.science/hal-03907148
Ed. Sheldon Axler et al. Springer Nature, 578 p., 2018, Universitext, 978-3-319-90274-6
https://www.springer.com/series/223
en
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
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
info:eu-repo/semantics/book
Books
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