Numerical Methods for SDEs

• First lecture: Tuesday, 23rd of April 2019, 14:15 - 15:45 in He18 room E.60.
• Additional lecture: Wednesday, 24th of April 2019, 14:15 - 15:45 in N24 room 131.
• First exercise class: Wednesday, 8th of May 2019, 14:15 - 15:45 in N24 room 131.

Students will learn algorithms for strong approximation and quadrature of solutions of stochastic differential equations (SDEs), their theoretical properties and typical applications. Topics cover:

• Existence, uniqueness and properties of solutions of SDEs.
• Algorithms for strong approximation of solutions of SDEs:
  • Euler-Maruyama scheme,
  • Milstein scheme,
  • high order strong Itô-Taylor schemes.
• Algorithms for quadrature of solutions of SDEs:
  • standard Monte Carlo methods,
  • multilevel Monte Carlo methods,
  • PDE approach based on the Feynman-Kac formula.
• Lower error bounds.

• SWS: 4+2
• ECTS: 9
• Type
  • Master Mathematik (optional)
  • Master Wirtschaftsmathematik (optional)
  • Master Mathematische Biometrie (optional)
  • Master of Finance (optional)
  
  
• Prerequisites
  • Analysis 1 and 2, Linear Algebra 1 and 2, Elementary Probability and Measure Theory or Introduction to Measure Theoretic Probability, and Stochastic Analysis.

Oral exam of 20 minutes.

To participate in the oral exam, you have to register at campusonline.uni-ulm.de.

The exercise sheets will be provided on Moodle.

• P. Kloeden & E. Platen, Numerical solutions of stochastic differential equations, Springer 1999.
• X. Mao, Stochastic differential equations and applications, Woodhead Publishing, 2011.
• T. Müller-Gronbach, E. Novak & K. Ritter, Monte Carlo-Algorithmen, Springer 2012.

You can also find the literature in the Semesterapparat.