## Arnulf Jentzen: Catalogue data in Autumn Semester 2017 |

Name | Dr. Arnulf Jentzen |

Field | Applied Mathematics |

URL | http://www.sam.math.ethz.ch/~jentzena |

Department | Mathematics |

Relationship | Assistant Professor |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

401-4657-00L | Numerical Analysis of Stochastic Ordinary Differential Equations Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods" | 6 credits | 3V + 1U | A. Jentzen | |

Abstract | Course on numerical approximations of stochastic ordinary differential equations driven by Wiener processes. These equations have several applications, for example in financial option valuation. This course also contains an introduction to random number generation and Monte Carlo methods for random variables. | ||||

Objective | The aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues. | ||||

Content | Generation of random numbers Monte Carlo methods for the numerical integration of random variables Stochastic processes and Brownian motion Stochastic ordinary differential equations (SODEs) Numerical approximations of SODEs Multilevel Monte Carlo methods for SODEs Applications to computational finance: Option valuation | ||||

Lecture notes | Lecture Notes are available in the lecture homepage (please follow the link in the Learning materials section). | ||||

Literature | P. Glassermann: Monte Carlo Methods in Financial Engineering. Springer-Verlag, New York, 2004. P. E. Kloeden and E. Platen: Numerical Solution of Stochastic Differential Equations. Springer-Verlag, Berlin, 1992. | ||||

Prerequisites / Notice | Prerequisites: Mandatory: Probability and measure theory, basic numerical analysis and basics of MATLAB programming. a) mandatory courses: Elementary Probability, Probability Theory I. b) recommended courses: Stochastic Processes. Start of lectures: Wednesday, September 20, 2017 Date of the End-of-Semester examination: Wednesday, December 20, 2017, 13:00-15:00; students must arrive before 12:30 at ETH HG E 19. Room for the End-of-Semester examination: ETH HG E 19. Exam inspection: Monday, March 5, 2018, 13:00-14:00 at HG D 5.1 Please bring your legi. | ||||

401-5650-00L | Zurich Colloquium in Applied and Computational Mathematics | 0 credits | 2K | R. Abgrall, R. Alaifari, H. Ammari, R. Hiptmair, A. Jentzen, S. Mishra, S. Sauter, C. Schwab | |

Abstract | Research colloquium | ||||

Objective |