Numerical Probability
An Introduction with Applications to Finance
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Beschreibung
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.
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.
Written by an expert in the subject Covers discretization schemes of stochastic differential equations Includes over 150 exercises Contains an extensive bibliography
Autor*in
Gilles Pagès
Themen in »Numerical Probability«
Monte Carlo method variance reduction Quasi-Monte Carlo method stochastic differential equation discretization schemes Euler schemes Milstein schemes 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