Aims - This module aims to provide an introduction to the ideas underlying the calculation of risk from a Bayesian and frequentist standpoint, and the structure of rational, consistent decision making. It is primarily intended for third and fourth year undergraduate students and taught postgraduate students registered on the degree programmes offered by the Department of Statistical Science, or jointly with other departments. It also serves as an optional module for students taking the mathematics and statistics stream of the Natural Sciences degree.

Objectives - On successful completion of the module, a student should be able to understand and compute financial measures of risk, understand the concepts of decision theory, find appropriate probability models for risky events and check the validity of the underlying assumptions, and be familiar with methodology for detecting changes in risk levels over time.

Applications - The ideas introduced in this module provide a generic framework for thinking about risk and decision-making in the presence of uncertainty. As such, they can be applied in many diverse areas. The module will include examples from natural hazards and finance using the R statistical software package.

Content - Introduction to Bayesian inference: conditional probability, Bayes' theorem, elicitation of subjective probabilities. Statistical decision theory: expected loss, randomised and non-randomised decision rules, decision principles, comparison of decision rules. Measures of risk: Value-at-Risk, Expected Shortfall. Dependence modelling: copula theory and its applications. Extreme value theory: probability models for the occurrence of extreme events, block maxima, peaks-over-threshold. Time series approaches to modelling volatility and detecting/modelling change in risk over time: ARMA models, ARCH/GARCH models.

Key texts - Available from ReadingLists@UCL.

Module description

The aim of the module is to teach the students basic communication skills in Norwegian: speaking, reading, writing and understanding...