PART IIA - 2012/2013
3E3 – Modelling Risk
Basic probability theory and statistics and basic knowledge of using Excel of Microsoft
Modelling Risk, 2 lectures/week, weeks 1-8 Michaelmas term
The aim of the course is to provide students with an understanding of a range of management science modelling methods involving randomness, such as simulation models, forecasting methods, regression, queueing theory, Markov chains, portfolio analysis, and decision analysis. For each of the modelling areas students will not only be introduced to the mechanics of the technique, but also shown the types of situations in which the method is useful.
1.Review of probability and statistical reasoning (1L)
- Characteristics of specific distributions: The normal distribution and the central limit theorem, the exponential distribution and the lack-of-memory property
- Statistical reasoning: sampling distribution, parameter estimation, confidence intervals, hypothesis tests
2. Computational analysis of stochastic processes (3L)
- Computer models of randomness: Monte Carlo Simulation in spreadsheets
- Stochastic processes, discrete event simulation, random number generation, sampling from a distribution, goodness of fit test
- Design and validation of simulation models, statistical analysis of simulation results, benefits and limitations of simulation models.
3. Regression and Forecasting (2L)
- Simple linear regression analysis, least squares estimates, significance of a regression.
- Different methods for forecasting: moving average methods, exponential smoothing, modelling seasonality and trends.
4. Portfolio Management (2L)
- Basic portfolio concepts: securities, risk, arbitrage
- The Capital Asset Pricing Model
- Risk and expected return on a portfolio, and efficient frontier
5. Mathematical analysis of stochastic
- Discrete and continuous-time Markov chains, hitting times, invariant distributions
Steady state probabilities of birth and death processes
Queueing theory, Poisson arrival processes,
classification of queueing systems, steady state, performance measures,
Little’s formula, benefits and limitations of queueing theory.
6. Decision Analysis (4L)
- Events and decisions, decision trees, expected monetary value,
- Utility theory
- Basic financial market concepts: securities, risk, arbitrage
- Options pricing and real options analysis
On completion of the course students should be able to:
Understand basic concepts of probability and the
rationale behind statistical reasoning
Be able to calculate statistical measures like mean and
variance, and interpret these in realistic situations
Use confidence intervals to quantify risk
Forecasting and Regression
Forecast data using short range extrapolative
techniques such as exponential smoothing.
Know how to take account of seasonality when
Apply regression techniques to estimate the way in
which two variables are related.
Decision Analysis and Portfolio Management
- Be able to understand decision trees and how to apply them in decision making.
- Be able to understand investment strategies for portfolios.
- Be able to incorporate risk into investment and decision making.
Stochastic Models and Simulation
- Understand how discrete event simulation models are
constructed and when the use of such models is appropriate.
- Be able to analyse the results of a simulation experiment.
- Be able to describe a Markov chain and analyse its long-term behaviour and steady state distribution.
- Understand and use simple formulæ for queues in which
arrivals occur as a Poisson process.
- Paper 1: Statistics and simulation, Weeks 2-3
- Paper 2: Regression,forecasting,portfolio analysis and Markov chains, Weeks 5-6
- Paper 3: Queueing theory and decision Analysis, Weeks 8-9
Please see the Booklist for Part IIA Courses for references for this module.
Last updated: June 2012