## MA312-6-SP-CO:Contingencies II

The details
2024/25
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Current
Monday 13 January 2025
Friday 21 March 2025
15
16 May 2024

Requisites for this module
MA212
(none)
(none)
(none)

(none)

## Key module for

BSC N233 Actuarial Science (Including Placement Year),
BSC N233DT Actuarial Science (Including Placement Year),
BSC N323 Actuarial Science,
BSC N323DT Actuarial Science,
BSC N324 Actuarial Science (Including Year Abroad),
BSC N325 Actuarial Science (Including Foundation Year),
MSCIN399 Actuarial Science and Data Science,
BSC N333 Actuarial Studies,
BSC N333DT Actuarial Studies,
BSC N334 Actuarial Studies (Including Placement Year),
BSC N334DT Actuarial Studies (Including Placement Year),
BSC N335 Actuarial Studies (Including Year Abroad)

## Module description

This module covers the second part related to Contingencies of the Institute and Faculty of Actuaries CM1 syllabus (Actuarial Mathematics).

## Module aims

The aims of this module are:

• to build and extend the methods developed in Contingencies I

• to analyse in detail additional techniques used in pricing, reserving, assessing the profitability and evaluating insurance and pensions products.

## Module learning outcomes

By the end of the module, students will be expected to be able to:

1. Define and use actuarial functions involving two lives.

2. Describe and critically evaluate methods which can be used to model and value cashflows contingent upon competing risks, i.e. those involving multiple transition or multiple decrement events.

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

4. Demonstrate conceptual understanding of the principal forms of heterogeneity within a population and the ways in which selection can occur.

5. Describe and carry out profit testing of various insurance contracts (e.g. conventional whole life, term, endowment assurances, or with-profits contracts), incorporating multiple decrement models as appropriate.

6. Implement life contingencies in Microsoft Excel spreadsheet, using some of Excel's built-in financial and statistical functions and other useful tools.

## Module information

Indicative syllabus

• 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.

• 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.

• 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.

• 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.

• Implement life contingencies in Microsoft Excel spreadsheet, using some of Excel's built-in financial and statistical functions and other useful tools.

## Learning and teaching methods

Teaching in the School will be delivered using a range of face to face lectures, classes and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.

## Bibliography*

The above list is indicative of the essential reading for the course.
The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students.

## Assessment items, weightings and deadlines

Coursework / exam Description Deadline Coursework weighting
Coursework   Test
Exam  Main exam: In-Person, Open Book (Restricted), 120 minutes during Summer (Main Period)
Exam  Reassessment Main exam: In-Person, Open Book (Restricted), 120 minutes during September (Reassessment Period)

### Exam format definitions

• Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
• In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
• In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
• In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary, for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.

Coursework Exam
30% 70%

### Reassessment

Coursework Exam
30% 70%
Module supervisor and teaching staff
Dr Jackie Wong Siaw Tze, email: jw19203@essex.ac.uk.
Dr Jackie Wong
maths@essex.ac.uk

Availability
Yes
Yes
No

## External examiner

Dr Melania Nica
Resources
Available via Moodle
No lecture recording information available for this module.

Further information

* Please note: due to differing publication schedules, items marked with an asterisk (*) base their information upon the previous academic year.

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