Quantitative Methods for Risk Management

Learning Outcomes

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• demonstrate knowledge and understanding of structure of uncertainty and risk, value at risk and conditional value at risk, decision analysis, utility theory and stochastic optimization
• demonstrate writing skills
• develop and analyse stochastic programming models for portfolio optimization, network capacity expansion
• utilise suitable mathematical methods to solve these models;
• structure practical problems
• analyse and quantify risks in finance and management sciences with some well-known methods and techniques such as VaR, CVaR and stochastic programming
• build models for simple problems in managerial decision making under uncertainty

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Appreciate the sources of risk in business, such as supply chain risks, project risk, technology risk and others;
• Analyse risk situations and dynamics considering the pluralistic nature of risk management;
• Critically analyse quantitative risk management methods context and challenges regardless of the industry.

Transferable and Generic Skills

Having successfully completed this module you will be able to:

• Appreciate the complexity of actual business world and how quantitative risk methods can improve business performance;
• Organize, present and communicate your professional and academic views in written form.
• Develop analytical and critical approaches to quantitative risk analysis;

1. Structure of uncertainty and risk: probability of a risky event, intersection risk, union risk, using sampling to reduce uncertainty – Bayesian method, portfolio risk

2. Measuring risk: Value at risk and conditional value at risk, generic risk measures, coherent risk measures, application of the risk measures to simple problems in financial investment and using copulas to model multivariate distributions.

3. Decision analysis: utility theory, stochastic dominance models, St. Petersburg paradox, Allais paradox

4. Stochastic modelling and analysis: Markowitz portfolio optimization model, newsvendor problem, two stage stochastic programming model for network capacity expansion, two stage stochastic programming recourse models for production planning, two stage Stakelberg leader follower model, sample average approximation, robust approaches for stochastic optimization

5. Using Monte Carlo simulation to value real options

The knowledge and appreciation of the theoretical bases will be developed through the lectures and complemented through directed reading and formative exercises.

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Repeat

An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.