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# MATH6158 Managing Uncertainty and Risk

## Module Overview

The module introduces some widely used quantitative approaches for characterizing uncertainty and risks in finance and management problems. The aim of the module is to introduce a number of widely used techniques for uncertainty and risk management and provide an understanding of how they can be used in practice.

### Aims and Objectives

#### Module Aims

To introduce a number of widely used techniques for uncertainty and risk management and provide an understanding of how they can be used in practice.

#### Learning Outcomes

##### Learning Outcomes

Having successfully completed this module you will be able to:

• 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
• 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
• utilise suitable mathematical methods to solve these models
• structure practical problems
• develop and analyse stochastic programming models for portfolio optimization, network capacity expansion
• demonstrate writing skills

### Syllabus

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. 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

### Learning and Teaching

#### Teaching and learning methods

The module will be delivered through lectures

TypeHours
Teaching16
Independent Study59
Total study time75

#### Resources & Reading list

Anderson EJ (2014). Business Risk Management: Models and Analysis.

### Assessment

#### Assessment Strategy

Feedbacks on exam will be generic and posed on the Blackboard

#### Summative

MethodPercentage contribution
Exam  (2 hours) 100%

#### Referral

MethodPercentage contribution
Exam 100%

#### Repeat Information

Repeat type: Internal & External

### Linked modules

Pre-requisites: MATH6006 AND MATH6002 or equivalent study in probability, statistics and optimisation

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