Aims

The aims of the course are to:

• Provide an understanding of the mechanics of a range of management science modelling methods involving randomness, such as statistics, decision analysis, portfolio management, queueing theory, Markov chains, dynamic programming, forecasting, & regression.
• For each of the modelling areas, students will become familiar with the types of situations in which the method is useful.

Objectives

As specific objectives, by the end 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.
• Conduct hypothesis testing.
• Be able to understand decision trees and how to apply them in decision making.
• Be able to describe a Markov chain and analyse its long-term behaviour and steady state distribution.
• Understand and use simple formulas for queues in which arrivals occur as a Poisson process.
• Be able to model staged decisions by dynamic programming and to solve some dynamic programs using value iteration and policy iteration algorithms.
• Forecast data using short range extrapolative techniques such as exponential smoothing.
• Know how to take account of seasonality when forecasting.
• Apply regression techniques to estimate the way in which two variables are related.
• Be able to understand investment strategies for portfolios.
• Be able to incorporate risk into investment and decision making.

Content

Review of Probability and Statistical Reasoning (2L)

• 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 testing.

Decision Analysis (2L)

• Events and decisions, decision trees, expected monetary value, sensitivity analysis, expected value of perfect information, expected value of sample information.

Mathematical Analysis of Stochastic Processes (6L)

• Dynamic programming: Bellman optimality equations, deterministic dynamic programming, probabilistic dynamic programming, value iteration algorithm, policy iteration algorithm.
• Markov chains: Discrete and continuous-time Markov chains, hitting times, steady-state 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.

Regression Analysis and Forecasting (4L)

• Simple linear regression analysis, least squares estimates, significance of  regression, multiple regression, multi-collinearity.
• Different methods for forecasting: moving average, exponential smoothing, modelling seasonality and trends.

Portfolio Management (2L)

• Basic portfolio concepts: securities, risk, arbitrage.
• The Capital Asset Pricing Model.
• Risk and expected return on a portfolio, and the efficient frontier.

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

 
Last modified: 03/08/2017 15:36