In this course, students will learn about various mathematical and statistical concept that are important in financial risk management.

(LO1) Apply convex analysis to solve mean-variance portfolio optimisation problems and discuss the outcomes

(LO2) Evaluate and select appropriate risk measures for a given financial application.

(LO3) Determine, approximate and/or estimate the loss distribution in a model with several risk factors

(LO4) Apply risk models exhibiting dependence to compute quantities of interest and interpret the outcomes

(LO5) Compute default probabilities and loss distributions in credit risk models and interpret the outcomes

(LO6) Implement in appropriate software, the methods for computing various quantities of interest in quantitative risk management and visualise and interpret the output

(S1) Analytical and problem-solving skills

(S2) Digital fluency

(S3) Effective communication with a range of stakeholders

1)Review of basic probability theory:
- Probability measures
- Random variables
- Expectation of a random variable
- Joint distribution of a pair of random variables
- Conditional expectation
- Independence

2)Mean-variance portfolio theory
- Portfolio return
- Portfolio variance
- Mean-variance analysis
- Portfolio selection problem
- Utility function
- CAPM

3)Risk measures
- Loss random variables and distributions
- Quantile, VaR, TVaR
- Properties of risk measures

4)Multivariate models for market risk
- Risk factors and aggregate risks
- Multivariate normal distributions
- Normal mixture distributions
- Normal variance mixtures and risk management

5)Modeling dependence via copulas
- Definition of copulas and Sklar’s theorem
- Archimedean copulas
- Dependence and copulas

6) Credit risk management
- Introduction
- Modeling individual default probabilit ies, and loss given default
- Modeling dependence between defaults