This module covers 25%, 30% and 20% of required material for the Institute and Faculty of Actuaries CS1, CS2 and CM2 syllabus, respectively.
Indicative syllabus
Bayesian Statistics (including decision theory and extreme value theory) [CS1, CS2-1.1,1.2, CS2-1.4]
1. Use Bayes’ theorem to calculate simple conditional probabilities.
2. Prior, posterior distributions, and conjugate prior distribution.
3. Choice of prior: conjugate families of distributions, vague and improper priors. Predictive distributions. Bayesian estimates and intervals for parameters and predictions. Bayes factors and implications for hypothesis tests. Understanding credibility theory using Bayesian framework.
4. Loss functions and Bayesian estimates, including explain the concepts of decision theory and apply them; loss, risk, admissible and inadmissible decisions, randomised decisions; minimax decisions and Bayes’ solutions, including simple results; calculate probabilities and moments of loss distributions.
Ruin theory [CM2-5.1,5.2,5.3]
1. Construct risk models involving frequency and severity distributions and calculate the moment generating function and the moments for the risk models both with and without simple reinsurance arrangements.
2. Explain the concept of ruin for a risk model.
3. Compound distributions and their applications in risk modelling
4. Explain what is meant by the aggregate claim process and the cash-flow process for a risk.
5. Define a compound Poisson process and define the probability of ruin in infinite/finite and continuous/discrete time and state and explain relationships between the different probabilities of ruin.
6. Describe and apply techniques for analysing a delay (or run-off) triangle and projecting the ultimate position, under GLM (how GLM underpin run-off triangle methodology). Describe and apply a basic chain ladder method for completing the delay run-off triangle using development factors, for estimating outstanding claim amounts.
Predictive modelling [CS1, CS2-5.1]
1. Generalised linear model: fundamental concepts of (GLM)
2. Define an exponential family of distributions. Show that the following distributions may be written in this form: binomial, Poisson, exponential, gamma, normal.
3. State the mean and variance for an exponential family and define the variance function and the scale parameter. Explain what is meant by the link function.
4. Explain what is meant by a variable, a factor taking categorical values. Define the linear predictor, illustrating its form for simple models, including polynomial models and models involving factors.
5. Define the deviance and scaled deviance and state how the parameters of a generalised linear model may be estimated. Apply statistical tests to determine the acceptability of a fitted model: Pearson’s chi-square test.
6. Fit a generalised linear model to a data set in R and interpret the output.
7. Understand extreme value distributions, suitable for modelling the distribution of severity of loss and their relationships; understand how to use extreme value distributions to model distribution tail weight.
8. Machine learning: explain the main branches of machine learning and describe examples of the types of problems typically addressed by Machine Learning.
9. Describe and give examples of key supervised and unsupervised Machine Learning techniques, explaining the difference between regression and classification and between generative and discriminative models.
10. Explain in detail and use appropriate software to apply Machine Learning techniques in R to simple problems.