Stochastic processes and their classification into different types by time space, state space, and distributional properties; construction of stochastic processes from finite-dimensional distributions, processes with independent increments, Poisson processes and renewal processes and their applications in general insurance and risk theory, Markov processes, Markov chains and their applications in life insurance and general insurance, extensions to more general intensity-driven processes, counting processes, semi-Markov processes, stationary distributions. Determining transition probabilities and other conditional probabilities and expected values; Integral expressions, Kolmogorov differential equations. Survival models - the random life length approach and the Markov chain approach; survival function, conditional survival function, mortality intensity, some commonly used mortality laws. Thiele's equation.
Statistical inference for life history data; Maximum likelihood estimation for parametric models.