The objectives of this class are two-fold. Half of the sessions are dedicated to classic probability (and correspond to about two thirds of the syllabus of SOA exam P) and half of the sessions provide an introduction to stochastic processes. The student who attends this class gains knowledge about all the necessary tools that are prerequisite to the study of option pricing and hedging. This class is also useful to those who contemplate furthering their studies in risk management or actuarial science.
The contents are as follows. Quick reminders on set theory. Independent and mutually exclusive events. Bayes theorem and law of total probability. Moments, including high-order moments, of probability distributions. Main probability distributions. Brownian motion. Martingales and Markov processes. Stochastic differential equations. Ito’s lemma. Girsanov’s theorem. Change of numéraire.