MAT 3104 Random Processes to Financial Mathematics

STAFFING:

REQUISITES:

RATIONALE:

Of fundamental importance to science, finance and engineering, are processes with random effects. The analysis of queues is one example of the modelling of random transitions. Some graduates will work in financial and commercial applications of mathematics where stochastic differential equations (SDEs) are of fundamental importance. SDEs also apply in many other areas in science and engineering and have many qualitatively new characteristics. Developing technical communication is also essential as preparation for the workplace.

SYNOPSIS:

This course begins by developing the modelling of processes with random effects. The application is developed to the classification and performance of queues subject to fluctuations in arrivals and services. Stochastic differential equations reflect volatilty in finance and occur in other areas. The course establishes a basic mathematical foundation for SDEs, shows some analytic solutions, and develops simple numerical schemes for simulation. Throughout the course basics of technical communication in the mathematical sciences are developed. This course is offered only in odd numbered years.

OBJECTIVES:

On completion of this course students will be able to:

1. understand random processes of various types including discrete time Markov chains, the Poisson process and birth/death process;
2. apply Markov queue techniques in science, finance and engineering problems;
3. solve and interpret classes of stochastic differential equations (SDEs);
4. construct and justify numerical schemes to simulate SDEs;
5. apply SDEs to solve some problems in financial applications;
6. structure, prepare and deliver documents and presentations of technical material.

TOPICS:

TEXT and MATERIALS required to be PURCHASED or accessed:

ALL textbooks and materials are available for purchase from USQ BOOKSHOP (unless otherwise stated). Orders may be placed via secure internet, free fax 1800642453, phone 07 46312742 (within Australia), or mail. Overseas students should fax +61 7 46311743, or phone +61 7 46312742. For costs, further details, and internet ordering, use the 'Textbook Search' facility at http://bookshop.usq.edu.au click 'Semester', then enter your 'Course Code' (no spaces).

Access to computer or internet facilities for mathematical typesetting.

REFERENCE MATERIALS:

Department of Mathematics and Computing CDROM SET 2, 2005 (availabel from the USQ Bookshop). This CD set contains course material, Windows and Linux Software relevant to this course offering. For more information about the CD sets and their use, please refer to http://www.sci.usq.edu.au/cdrom and the course web site.

STUDENT WORKLOAD REQUIREMENTS:

ASSESSMENT DETAILS:

NOTES:

1.

Examination dates will be available during the semester. Please refer to the examination timetable when published.

IMPORTANT ASSESSMENT INFORMATION

1. Attendance requirements:
   It is the students' responsibility to attend and participate appropriately in all activities (such as lectures, tutorials, laboratories and practical work) scheduled for them, and to study all material provided to them or required to be accessed by them to maximise their chance of meeting the objectives of the course and to be informed of course-related activities and administration.
2. Requirements for students to complete each assessment item satisfactorily:
   To complete each of the assessment items satisfactorily, students must obtain at least 50% of the total marks available for each assessment item.
3. Penalties for late submission of required work:
   If students submit assignments after the due date without prior approval then a penalty of 20% of the total marks gained by the student for the assignment will apply for each working day late.
4. Requirements for student to be awarded a passing grade in the course:
   To be assured of a passing grade, students must demonstrate, via the summative assessment items, that they have achieved the required minimum standards in relation to the objectives of the course by: (i) satisfactorily completing the examination and assignments; and (ii) obtaining at least 50% of the total weighted marks available for all summative assessment items. Students who do not qualify for a Passing grade may, at the discretion of the Examiner, be awarded a Supplementary Examination and/or assigned additional work to demonstrate to the Examiner that they have achieved the required standard. It is expected that such students will have gained at least 45 % of the total marks available for all summative assessment items.
5. Method used to combine assessment results to attain final grade:
   The final grades for students will be assigned on the basis of the weighted aggregate of the marks obtained for each of the summative assessment items in the course.
6. Examination information:
   In an Open Examination, candidates may have access to any material during the examination except the following: electronic communication devices, bulky materials, devices requiring mains power and material likely to disturb other students.
7. Examination period when Deferred/Supplementary examinations will be held:
   Any Deferred or Supplementary examinations for this course will be held during the examination period at the end of the semester of the next offering of this course.
8. University Regulations:
   Students should read USQ Regulations 5.1 Definitions, 5.6. Assessment, and 5.10 Academic Misconduct for further information and to avoid actions which might contravene University Regulations. These regulations can be found at the URL http://www.usq.edu.au/corporateservices/calendar/part5.htm or in the current USQ Handbook.

ASSESSMENT NOTES