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School of Mathematics

# MATH20962 - 2009/2010

General Information
• Title: Contingencies 1
• Unit code: MATH20962
• Credit rating: 10
• Level: 2
• Pre-requisite units: MATH10951, MATH20962, MATH20702
• Co-requisite units: None
• This course unit may only be taken by students on the Actuarial Science and Mathematics degree programme
• School responsible: Mathematics
• Members of staff responsible: Mrs Giselle Du Toit
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## Unit specification

### Aims

The unit aims to provide a mathematical introduction to models using cashflows which depend upon survival, death and other uncertain factors.

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### Syllabus

This unit explores some further simple financial topics from a mathematical point of view.

1. Introduction to Survival Models, Markov Jump Processes and the Cox regression model. This material is covered more fully in the units devoted to CT4 but is introduced here as this unit builds upon it. (3 lectures)
2. Annuities and Assurances. Definition of simple contracts. Means and variances of the present values of benefits in discrete and continuous time. Definitions of standard symbols and derivation of relationships between them. (5-6 lectures)
3. Life table. Patterns of mortality. Evaluation of means and variances using the life table. Approximations for means and variances in continuous time. Select mortality. (4-5 lectures)
4. Net premiums and reserves. Net future loss random variable and equivalence principle. Equivalence of prospective and retrospective reserves. Recursive relationships. Thiele’s Differential Equation. Mortality profit and its analysis. (3-4 lectures)
5. Variable Benefits and Annuities. Payments varying at a constant compound rate and by a constant monetary amount. With-profit contracts. (2 lectures)
6. Gross premiums and reserves. Expenses and effect of inflation. Gross future loss random variable and the equivalence principle. Equivalence of prospective and retrospective reserves. Recursive relationships. (3-4 lectures)

### Textbooks

• Core Reading : Subject CT5, Contingencies. Produced by the Actuarial Profession
• NL Bowers, Actuarial Mathematics, HU Gerber and JC Hickman, Society of Actuaries, 1997

### Learning and teaching processes

Two lectures per week in weeks 1-11 of semester 2. (22 lecture hours)
Tutorial in weeks 2-12. (11 tutorial hours)
Private Study (67 hours)

### Assessment

Coursework Assignment. Will include questions involving short reports. weighting 20%,
Examination at end of semester 2, 2 hours duration, weighting 80%.

## Arrangements

Online course materials are available for this unit.