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CMPC1F07 - MATHEMATICS FOR ACTUARIES

Module Code:
CMPC1F07
Department:
Computing Sciences
Credit Value:
20
Level:
1
Organiser:
Dr. Katharina Huber
This module introduces key concepts in set theory, linear algebra and core financial mathematics for actuarial science or business statistics students. THIS MODULE IS RESERVED FOR STUDENTS ON ACTUARIAL SCIENCES AND BUSINESS STATISTICS ONLY.
  • Gersting,J.L., Mathematical Structures for Computer Science, Freeman
  • Kellison,S.G., The Theory of Interest. 2nd ed. Homewood
  • McCutcheon,J. J. and Scott,W. F. An introduction to the Mathematics of Finance. Heinemann - Essential purchase
  • Formulae and tables, available from the Institute of Actuaries publications shop Essential purchase

Submission:

Written coursework should be submitted by following the standard CMP practice. Students are advised to refer to the Guidelines and Hints on Written Work in CMP.

Deadlines:

If coursework is handed in after the deadline day or an agreed extension:
 

Work submitted Marks deducted
After 15:00 on the due date and before 15:00 on the day following the due date 10 marks
After 15:00 on the second day after the due date and before 15:00 on the third day after the due date 20 marks
After 15:00 on the third day after the due date and before 15:00 on the 20th day after the due date.  All the marks the work merits if submitted on time (ie no marks awarded) 
After 20 working days Work will not be marked and a mark of zero will be entered


Saturdays and Sundays will NOT be taken into account for the purposes of calculation of marks deducted.

All extension requests will be managed through the LTS Hub. A request for an extension to a deadline for the submission of work for assessment should be submitted by the student to the appropriate Learning and Teaching Service Hub, prior to the deadline, on a University Extension Request Form accompanied by appropriate evidence. Extension requests will be considered by the appropriate Learning and Teaching Service Manager in those instances where (a) acceptable extenuating circumstances exist and (b) the request is submitted before the deadline. All other cases will be considered by a Coursework Coordinator in CMP.

For more details, including how to apply for an extension due to extenuating circumstances download Submission for Work Assessment (PDF, 39KB)
 

Plagiarism:

Plagiarism is the copying or close paraphrasing of published or unpublished work, including    the work of another student; without due acknowledgement. Plagiarism is regarded a serious offence by the University, and all cases will be investigated. Possible consequences of plagiarism include deduction of marks and disciplinary action, as detailed by UEA's Policy on Plagiarism and Collusion.


 


Module specific

The objectives of this module are to give students an:

  • Ability to analyse problems, by formulating them mathematically and solving them using the techniques covered in the unit,
  • Introduction to use of mathematics in finance

Transferable skills

Students will gain:

  • Competence in using sets and linear algebra to represent and solve problems
  • Competence in core mathematics and its application in finance

Subject specific:

On completion of this module students will have:

  • Understanding of sets, relations and functions
  • Understanding of linear algebra and its use to represent and solve equations 
  • A good understanding of core financial mathematics meeting the requirements of the Actuarial professional examination, CT1 enabling students to:

-Describe how to use a generalised cashflow model to describe financial transactions.
-Describe how to take into account the time value of money using compound interest and discounting.

-Show how interest rates may be expressed in terms of different  time periods.
-Demonstrate a knowledge and understanding of real and money interest rates and the term structure of interest rates.

-Calculate the present and accumulated values of a stream of equal or unequal payments. Calculate the delivery price and value of a forward contract using arbitrage-free pricing.
-Define the main compound interest functions (including annuities certain).

-Define an equation of value.
-Describe how loans may be repaid and show how discounted cashflow techniques can be used in project appraisal.

-Describe the investment and risk characteristics of the main asset types.
-Analyse elementary compound interest problems.


 

Total hours: 48 (Lectures and seminars)

Every week the class will meet for 4 hours, two hours on financial mathematics and two hours on the remainder of the syllabus; regular exercise sheets will be set and reviewed.

The material covered in this unit will cover the topics listed below; it is not intended to reflect a detailed presentation order. The lectures/seminars (4 per week) are used to motivate the topics and give a general overview as well as the vehicle for detailed explanations of the techniques and going over set exercises. 2 hours of the course are allowed for the course test. In the last week, there are only 2 hours of lecture.

  1. Linear Algebra (10 lectures/seminars)

    Vectors over the reals: Addition, scalar multiplication; scalar product; vector algebra; Geometric interpretation of vectors
    Matrices: submatrices; matrix arithmetic;
    Systems of linear equations:
    equivalent systems of equations; Solution of systems of linear equations; Gaussian elimination; inverse matrices;  Determinants; eigenvalues and their applications.

  2. Sets, Relations and Functions (10 lectures/seminars)

    Sets and subsets:Venn diagrams. Operations with sets. Laws. Cartesian products;
    Relations: Binary relations. Reflexive, symmetric, antisymmetric, transitive relations; Graphical and Boolean matrix representation and simple algorithms.
    Functions: One-to-one, onto and bijective. Inverse functions. Functions of more than one argument.

  3. Financial mathematics (24 lectures)

  • Generalised cashflow model; compound interest and discounting; real and money interest rates;
  • Values of investments allowing for interest and inflation;
  • Compound interest functions including annuities certain;
  • Equations of value; loan repayment modelling;
  • Use of discounted cashflow techniques in investment project appraisal;
  • Value of a forward contract using arbitrage free pricing methods;
  • Structure of interest rates;
  • Simple stochastic models for investment returns
  • These lectures will cover most of the syllabus for the professional exam of the Faculty of Actuaries/ Institute of Actuaries CT1: Financial Mathematics Core Technical.

 


Examination with Coursework or Project