Numerical Probability An Introduction with Applications to Finance /

• Main Author: Pagès, Gilles (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Universitext,
• Subjects: Probabilities.; Economics, Mathematical .; Statistics .; Probability Theory and Stochastic Processes.; Quantitative Finance.; Statistics for Business, Management, Economics, Finance, Insurance.

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 development...

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.