%0 Book
%T Numerical Probability
%T An introduction with applications to Finance
%+ Laboratoire de Probabilités, Statistique et Modélisation (LPSM (UMR_8001))
%A Pagès, Gilles
%Z Autres éditeurs de la collection : Carles Casacuberta, Angus MacIntyre, Kenneth Ribet, Claude Sabbah, Endre Süli,Wojbor A. Woyczyński
%@ 978-3-319-90274-6
%Y Ed. Sheldon Axler et al.
%I Springer Nature
%C Switzerland
%S Universitext
%P 578 p.
%8 2018-08
%D 2018
%K Monte Carlo method
%K variance reduction
%K Quasi-Monte Carlo method
%K stochastic differential equations
%K discretization schemes
%K Euler scheme
%K Milstein scheme
%K optimal vector quantization
%K stochastic approximation
%K multilevel extrapolation methods
%K Romberg extrapolation methods
%K pricing of derivative products
%K greeks sensitivity computation
%K tangent process and log-likelihood method
%K Malliavin Monte Carlo
%K risk measures
%K Value-at-Risk (conditional)
%K American options
%K least squares regression methods
%K quantization schemes
%Z Mathematics [math]/Probability [math.PR]Books
%X 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.
%G English
%L hal-03907148
%U https://cnrs.hal.science/hal-03907148
%~ UNIV-PARIS7
%~ CNRS
%~ INSMI
%~ USPC
%~ LPSM
%~ SORBONNE-UNIVERSITE
%~ SORBONNE-UNIV
%~ SU-SCIENCES
%~ UNIV-PARIS
%~ UP-SCIENCES
%~ ALLIANCE-SU