PART 1 - PROBABILITY
1.   DISTRIBUTIONS AND BASIC DISTRIBUTIONAL QUANTITIES
1.1.Random variable; distribution function; continuous, discrete and mixed random variables; hazard rate
1.2.Moments
1.3.Quantiles
1.4.Moment generating function and probability generating function
1.5.Sum of independent random variables
1.6.Tails of distributions
2.   CHARACTERISTICS OF ACTUARIAL MODELS
2.1.Parametric distributions and scale distributions
2.1.1. Scale, location and shape parameters
2.1.2. The linear exponential family
2.2.Mixed distributions
3. SEVERITY MODELS (CONTINUOUS MODELS)
3.1.Creating new distributions
3.2.Recognition of families of distributions and their relations
PART 2 - STOCHASTIC PROCESSES
4.  GENERAL NOTIONS OF STOCHASTIC PROCESSES
4.1.Some definitions
4.2.Specification of a stochastic process
4.3.Classification of a stochastic process
5.  DISCRETE TIME MARKOV CHAINS
5.1.Definitions
5.2.Transition probability matrices
5.3.First step analysis
5.4.Classification of states
5.5.Limit Behaviour
5.6.Applications to no claim discount and bonus-malus systems
6.  MARTINGALES
6.1.Definitions and examples
6.2.Stopping time
6.3.Kolmogorov inequality for nonnegative martingales and supermartingales
7.  BROWNIAN MOTION
7.1.Definitions
7.2.Markov property and the reflection principle
7.3.Variations and extensions
7.4.Martingales and hitting times
7.5.The Black-Scholes formula