Selected applications of probability

Basic Information

M125 (2+0+1) - 4 ECTS credits

To inform students about different applications of probability theory and stochastic models. To illustrate applications of theoretical concepts from probability theory and stochastic processes theory. Special focus will be on applications in other scientific areas, such as biology, economics, finance, actuarial mathematics and others.

You can access the course content at the following link: PDF

Teachers

 

Basic literature

  1. P. Embrechts, C. Klüppelberg, T. Mikosch, Modelling extremal events: for insurance and finance, Springer-Verlag, Berlin, 1997.

Additional literature

  1. J. Albert, J. Bennett, J. J. Cochran (editors), Anthology of statistics in sports. Society for Industrial and Applied Mathematics, 2005.
  2. H. Albrecher, S. Asmussen, Ruin probabilities, World Scientific, Singapore, 2010.
  3. T. R. Bielecki, M. Rutkowski, Credit risk: modeling, valuation and hedging. Springer Science & Business Media, 2013.
  4. W. M. Bolstad, J. M. Curran, Introduction to Bayesian statistics. John Wiley & Sons, 2016.
  5. D. Brigo, M. Morini, A. Pallavicini, Counterparty credit risk, collateral and funding: with pricing cases for all asset classes, John Wiley & Sons, 2013.
  6. R. Durrett, Probability models for DNA sequence evolution, Springer Science & Business Media, 2008.
  7. J. E. Gentle, Random number generation and Monte Carlo methods, Springer Science & Business Media, 2006.
  8. H. U. Gerber, E. S. W. Shiu, Optimal dividends: analysis with Brownian motion, North American Actuarial Journal 8(2004), 1-20
  9. T. Hastie, R. Tibshirani, J. Friedman, The Elements of Statistical Learning: Data Mining, Inference and Prediction, Springer, 2017.
  10. G. James, D. Witten, T. Hastie, R. Tibshirani, An Introduction to Statistical Learning with Applications in R, Springer, 2021.

Teaching materials

The materials are available on the internal Teams channel of the course, through which all internal communication takes place. Students are required to register on the course’s Teams channel. The channel code for joining the course can be found in the schedule.