"The aim of this course is to equip students with the skills to conduct simulations and perform mathematical convergence analysis for stochastic models, with applications in fields such as mathematical finance.
The course provides a comprehensive understanding of various numerical methods, covering their foundational principles, convergence properties, and practical implementation considerations." (from the official course's page)
The course has been taught at ETH Zurich by Professor Josef TeichmannJosef Teichmann and Dr Christoph Czichowsky
Feel free to reach out to me with any comments, clarifications, or corrections.
Index
- Mathematical Formulation of Random Number Generation
- Brownian Motion and Lévy Processes
- Stochastic Integration and Itô Calculus
- Stochastic Ordinary Differential Equations
- Numerical Approximations of SDEs
- Euler–Maruyama Scheme and Monte Carlo Methods
- Milstein Scheme, Stochastic Runge–Kutta, and Talay–Tubaro Extrapolation
- Stochastic Simulation and Monte Carlo Methods
- Euler–Maruyama for Lévy-Driven SDEs
- Multilevel Monte Carlo and Efficient Increment Simulation