Pensum
Vi skal bruke f?lgende pensumsb?ker i dette kurset:
1. P. Embrechts, C. Klüppelberg, T. Mikosch: Modelling Extremal Events: for Insurance and Finance. Springer (2012).
2. S.R.S. Varadhan: Large Deviations and Applications. Courant Institute of Mathematical Sciences (1994/2016).
St?ttelitteraturen vi trenger er:
3. A. McNeil, R. Frey, P. Embrechts: Quantitative Risk Management. Princeton Series in Finance (2015).
Pensum:
Det er planlagt ? gjennomg? f?lgende kapitler i boken til Embrechts, Klüppelberg, Mikosch om modellering av ekstreme hendelser:
1. Risk Theory (som innf?ring i sub-eksponentielle fordelinger)
2. Fluctuations of Sums
3. Fluctuations of Maxima
4. Fluctuations of Upper Order Statistics
5. An Approach to Extremes via Point Processes
6. Statistical Methods for Extremal Events
7. Time Series Analysis for Heavy-Tailed Processes (if time permits)
Vi skal ogs? ta gjennomgang av f?lgende kapitler i boken til Varadhan om store avvik:
2. Large Deviations
3. Cramer?s Theorem
4. Multidimensional Version of Cramer?s Theorem
5. An Infinite Dimensional Example: Brownian Motion
6. The Ventcel-Freidlin Theory