An introduction to stochastic processes and time series with a view towards the applications in finance and insurance.

Brownian motion (Wiener process);Definition and properties; construction of the stochastic integral and properties; Ito isometry and Ito formula;

Markov chains in discrete time; definition and fundamental formulas; application of the Markov property; classification of states;

introduction to time series analysis: stationary processes (in discrete time), auto covariance function, ARMA processes, estimation and forecasting.

Written and oral examination.
More information on: https://fam.tuwien.ac.at/lehre/pr/

• Z. Brzezniak and T. Zastawniak. Basic Stochastic Processes. Springer, 2007
• P. J. Brockwell and R. A. Davis. Introduction to time series analysis and forecasting. Springer, New York, 2. edition, 2002.
• R. Schlittgen and B. Streitberg. Zeitreihenanalyse. Oldenbourg, München; Wien, 9. edition, 2001.
• J.R. Norris. Markov Chains (Cambridge Series in Statistical and Probabilistic Mathematics). Cambridge University Press, 1998.