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MSc. Finance: Elective course in Financial Mathematics or Stochastic

MSc. Mathematics/WiMa: Elective course in Financial Mathematics

2+1 SWS, 4 Credit Points

News:

None, so far.

• Lecture: Wednesday, 10:00-12:00, He18 - 1.20
• First Lecture: 18/04/2017
• Exercise class: Friday, 10:00-12:00, He18 - E20, every two weeks.
• First Exercise class: 27/04/2017

Final Exam:

oral (no prerequisites). The oral exam takes 20 minutes.

To attend the oral exam in either Time Series Analysis or Lévy Processes, write an e-mail to Eva Nacca with the date picked from the following list which fits you the most. Mrs. Nacca will then write you the specific time when your exam is going to take places at this date. The possible dates with the probable times are:

• Monday, 16th July 2018, 12-15 pm.
• Thursday, 19th July 2018, 13-16 pm.
• Monday, 23rd July 2018, 12:30-15:30 pm.
• Tuesday, 24th July 2018, 13-16 pm.
• Tuesday, 31st July 2018, 13-16 pm.
• Thursday, 2nd August 2018, 13-16 pm.
• Tuesday, 14th August 2018, 10-14 pm.
• Friday, 17th August 2018, 10-14 pm.
• Wednesday, 29th August 2018, 10-14 pm.
• Thursday, 30th August 2018, 13-16 pm (fully booked).

Prerequisites:

Measure Theoretic Probability.

Contents:

This course covers the basic facts of time series analysis. Time series analysis is concerned with the description of true data through a stochastic model which is usually assumed to be stationary. The contents of the lecture include:

• Examples of Time Series
• Stationarity of Time Series
• Estimating Trend and Seasonal Components
• Properties of the Autocovariance Function
• Linear filters and Moving Average Processes of Infinite Order
•  ARMA Models
• Linear Prediction
• Estimation of the Mean and the Autocovariance
• Estimation for Causal Autoregressive Processes
• A Short Introduction to Spectral Theory

•           Wold decomposition (if time permits)

 Literature:

A list of reference books would cover the following works:

• P. J. Brockwell and R. A. Davis: Time Series: Theory and Methods. 2nd edition, Springer, 1991.
• P. J. Brockwell and R. A. Davis: Introduction to Time Series and Forecasting. 2nd edition, Springer, 2002.
•  J.-P. Kreiß and G. Neuhaus: Einführung in die Zeitreihenanalyse. Springer, 2006.
• W. A. Fuller: Introduction to Statistical Time Series. 2nd edition, Springer, 1996.

Exercise sheets: