Contingencies II

The details
Mathematical Sciences
Colchester Campus
Undergraduate: Level 6
Thursday 03 October 2019
Saturday 14 December 2019
27 October 2019


Requisites for this module



Key module for

BSC N233 Actuarial Science (Including Placement Year),
BSC N323 Actuarial Science,
BSC N324 Actuarial Science (Including Year Abroad),
BSC N325 Actuarial Science (Including Foundation Year)

Module description

The aim of the Contingencies II module is to build and extend the methods developed in Contingencies I to obtain additional techniques for use in pricing and evaluating insurance and pensions products and insurance companies. This module covers the second part of the Institute and Faculty of Actuaries CT5 syllabus (Contingencies, Core Technical).

Module aims


1. Simple assurances and annuities involving two lives
Define and use straightforward functions involving two lives and those that involve a fixed term as well as age. In respect of these functions: define assurance and annuity contracts and develop formulae for the means and variances of the present value of the payments under the contracts; define practical methods of evaluating means and variances under contracts; describe and calculate net premiums and net premium reserves; describe the calculation of net premiums and net premium reserves for increasing and decreasing benefits; and describe gross premiums and gross premium reserves [CT5-(vi)].

2. Competing risks
Describe methods that can be used to model cashflows contingent on competing risks: use of multiple-state Markov models; use of Kolmogorov equations; and derivation of transition intensities [CT5-(vii)].

3. Discounted cashflows
Describe the technique of discounted emerging costs for use in pricing, reserving and assessing profitability. Develop profit testing techniques for unit linked and traditional products; use profit testing for pricing and reserving; use multiple decrement tables and practical alternatives; and apply the techniques to cashflows dependent on non-human contingent risks [CT5-(viii)].

4. Mortality and morbidity
Describe the principal forms of heterogeneity within a population and the ways in which selection can occur. Describe the factors that affect human morbidity and mortality. Define and give examples of the main forms of selection: describe selection in the context of pension schemes and life assurance contracts; explain why it is necessary to have different mortality tables for different classes of lives; explain how decrements can have a selective effect; describe the use of risk classification, genetic information and a single figure index for measuring mortality in a population, with examples and illustrations of use [CT5-(ix)].

Module learning outcomes

On completion of this module, students should be able to:

Define and use straightforward functions involving two lives.

Describe methods which can be used to model cashflows contingent upon competing risks.

Describe the technique of discounted emerging costs, for use in pricing, reserving, and assessing profitability.

Describe the principal forms of heterogeneity within a population and the ways in which selection can occur.

Module information

No additional information available.

Learning and teaching methods

This module has 30 lectures in the autumn term. There are 3 revision lectures in the summer term.


This module does not appear to have a published bibliography.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Weighting
Coursework Homework 1 08/11/2019 10%
Coursework Homework 2 10/12/2019 10%
Exam 120 minutes during Summer (Main Period) (Main)

Overall assessment

Coursework Exam
20% 80%


Coursework Exam
0% 100%
Module supervisor and teaching staff
Nor Abdul Aziz (
Dr Spyridon Vrontos (



External examiner

Dr Dimitrina Dimitrova
Cass Business School, City, University of London
Senior Lecturer
Available via Moodle
Of 33 hours, 33 (100%) hours available to students:
0 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).


Further information
Mathematical Sciences

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