Computational Methods for Risk Analysis and Decision Making

Course Coordinator: Dr Tony MT Chan, Grad Dip, MPhil (CUHK), PhD (CityU)

Important note
This course will be taught through a face-to-face mode. The course will be presented in English. Lectures and tutorials will be scheduled on either weekday evenings, or Saturdays or Sundays afternoon.

MATH S812F is one of the core courses in the Master of Science in Quantitative Analysis and Computational Mathematics. It is also one of the courses in the Postgraduate Diploma in Quantitative Analysis and Computational Mathematics, and the Postgraduate Certificate in Computational Mathematics.

The course aims to develop students’ understanding of numerical methods and scientific computing techniques used to solve quantitative models related to differential equations, along with their applications to dynamics problems in science, engineering, quantitative risk analysis, financial Black–Scholes equations, option pricing and stochastic volatility models. This course also places emphasis on the numerical analysis of errors, accuracy, stability and computational complexity through various numerical examples.

Advisory prerequisite(s)
You are advised to have some background knowledge in mathematics and quantitative science, or a related discipline.

Aims
This course aims to:

• Teach various numerical methods for solving ordinary and partial differential equations;
• Enable students to formulate dynamics problems related to science, engineering, quantitative risk analysis, financial Black–Scholes equations and option pricing models;
• Teach students to use appropriate numerical techniques and scientific programs to solve problems and to analyse the results.

Contents
The course will cover the following topics:

• Numerical methods for solving ordinary differential equations
• Numerical methods for solving partial differential equations
• Formulation of computational models and scientific programs for their implementation and numerical analysis
• Black–Scholes models and mathematical analysis
• Option pricing models using implicit and explicit numerical methods
• Modelling dynamics problems and case studies

Learning support
There will be regular face-to-face lectures and tutorials throughout the course.

Course assessment
Course assessment will be divided into continuous assessment (50%) and a project (50%). The continuous assessment portion will include 2 compulsory Assignments (30%), and a report on the practical exercise (20%). The project will be evaluated based on the following components: (i) an oral presentation (20%), and (ii) a written final report (30%). Students are required to submit assignments via the Online Learning Environment (OLE).

Online requirement
This course is supported by the Online Learning Environment (OLE). You can find the latest course information from the OLE. Through the OLE, you can communicate electronically with your lecturer as well as other students. To access the OLE, you will need to have access to the Internet. The use of the OLE is required for the study of this course.

Equipment
Students will need access to a computer system suitable for connecting to the Internet. The recommended minimum computing requirements are:

• Pentium IV CPU
• SVGA display card and monitor
• 1 GB RAM
• 500MB free hard disk space
• Broadband Internet access

Set book(s)
Numerical Methods for Engineers and Scientists: An Introduction with Applications Using MATLAB, by Amos Gilat, Vish Subramaniam (2007), John Wiley and Sons.