Module Directory

This module introduces decision theory, loss distributions, risk modelling, Machine learning, Bayesian inference, comparative inference and the generalised linear model.

The aims of this module are:

• to learn the concept and basic principle of Bayesian inference.


• to learn the concept of decision theory.


• to learn the principles and methods of choosing good estimators.


• to learn the basic concept of ruin theory.


• to learn the basic random variables and distributions for risk modelling.


• to learn how to use R to implement Bayesian analysis.

By the end of the module, students will be expected to:

1. Understand concepts of decision theory.


2. Understand concepts of ruin theory and distributions for risk models.


3. Understand techniques for analysing a delay (or run-off) triangle and projecting the ultimate position.


4. Have a deep understanding of basic principles of Bayesian estimation with extension to group decision and empirical prior.


5. Have a deep understanding of principles and methods to choose good estimators.


6. Apply R for the Bayesian analysis. 

Indicative syllabus

Bayesian Statistics (including decision theory) [CS1-5]

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.


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.


5. Understanding credibility theory using Bayesian framework.


6. Understanding group decision in prior and empirical prior.

Random variables and distributions for Risk modelling [CS2-1.1,1.2, 1.3]

1. Construct risk models involving frequency and severity distributions


2. Calculate the moment generating function and the moments for the risk models.


3. Describe the operation of simple forms of proportional and excess of loss reinsurance


4. Distributions for modelling aggregated loss


5. Compound distributions and their application in risk modelling; compound Poisson distribution; insurance and reinsurance modelling


6. Introduction to extreme value theory.

Liability valuation [CM2-5]

1. Explain the concept of ruin for a risk model.


2. Explain what is meant by the aggregate claim process and the cash-flow process for a risk.


3. 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.


4. Describe and apply techniques for analysing a delay (or run-off) triangle and projecting the ultimate position. Describe and apply a basic chain ladder method for completing the delay run-off triangle using development factors, for estimating outstanding claim amounts.

Teaching in the School will be delivered using a range of face to face lectures, classes and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.