Basic measure theory, probability measures, expectations, conditional expectations, martingales. Basics in large deviations theory, heavy tailed processes.

References:
1)      Probability, A. N. Shiryaev, 2000, Springer
2)      Probability and Martingales, D Williams, 1991, Cambridge
3)      Probability: Theory and Examples, R Durrett, 2010, Cambridge
4)      Large Deviations Techniques and Applications. 1998. Dembo and Zeitounni. Springer.
5)      Modelling Extremal Events for Insurance and Finance. 1997.  Embrechts, Klüppelberg and Mikosch. Springer