Assuming a uniform distribution of deaths, define the continuous survival-time random variable that arises from the discrete survival-time random variable.
Define severity random variables
with or without a deductible;
with or without a limit;
with or without coinsurance.
For any survival-time or severity random variable defined above, with single or mixed distributions, calculate
expected values;
variances;
probabilities;
percentiles.
Define non-homogeneous and homogeneous discrete-time Markov Chain models and calculate the probabilities of
being in a particular state;
transitioning between particular states.
Frequency models.
Define and calculate expected values, variances and probabilities for frequency random variables
under the Poisson distribution;
under the Binomial distribution;
under the Negative Binomial distribution;
under the Geometric distribution;
under any mixture of the above.
Define and calculate expected values, variances and probabilities for Poisson processes,
using increments in the homogeneous case;