MA312-7-SP-CO:
Contingencies II
2021/22
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Postgraduate: Level 7
Current
Monday 17 January 2022
Friday 25 March 2022
15
12 May 2021
Requisites for this module
(none)
(none)
(none)
(none)
(none)
DIP N32309 Actuarial Science,
MSC N32312 Actuarial Science
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 part the second part of the Institute and Faculty of Actuaries CM1 syllabus (Actuarial Mathematics).
The aims of this module are:
1.to critically analyse simple assurances and annuities involving two lives;
2. to examine in detail competing risks;
3. to develop in detail the use of discounted cashflows;
4. to critically analyse mortality and morbidity modelling;
5. to implement life contingencies in Microsoft Excel spreadsheet.
On completion of this module, students should be able to:
1. Define and use straightforward functions involving two lives.
2. Describe methods which can be used to model cashflows contingent upon competing risks.
3. Describe the technique of discounted emerging costs, for use in pricing, reserving, and assessing profitability.
4. Describe the principal forms of heterogeneity within a population and the ways in which selection can occur.
5. Critically analyses the techniques used for pricing contingencies.
6. Implement life contingencies in Microsoft Excel spreadsheet, using some of Excel's built-in financial and statistical functions and other useful tools.
(i) Define and use functions involving two lives.
1. Techniques to deal with cash flows dependent upon the death or survival of either or both of two lives.
2. Techniques to deal with functions dependent upon a fixed term as well as age.
(ii) Describe and illustrate methods of valuing cash flows that are contingent upon multiple transition events.
1. Define health insurance, and describe simple health insurance premium and benefit structures.
2. Explain how a cash flow, contingent upon multiple transition events, may be valued using a multiple-state Markov Model, in terms of the forces and probabilities of transition.
3. Construct formulae for the expected present values of cash flows that are contingent upon multiple transition events, including simple health insurance premiums and benefits, and calculate these in simple cases. Regular premiums and sickness benefits are payable continuously and assurance benefits are payable immediately on transition.
(iii) Describe and use methods of projecting and valuing expected cash flows that are contingent upon multiple decrement events.
1. Define a multiple decrement model as a special case of multiple-state Markov model.
2. Derive dependent probabilities for a multiple decrement model in terms of given forces
of transition, assuming forces of transition are constant over single years of age.
3. Derive forces of transition from given dependent probabilities, assuming forces of transition are constant over single years of age.
4. Describe the construction and use of multiple decrement tables.
5. Describe the typical benefit and contribution structures of pension schemes, including:
* defined contribution schemes
* defined benefit (final salary) schemes
6. Use multiple decrement tables to evaluate expected present values of cash flows
dependent upon more than one decrement, including those of pension schemes.
(iv) Describe and use projected cash flow techniques, where and as appropriate for use in pricing, reserving, and assessing profitability.
1. Define unit-linked contract.
2. Project expected future cash flows for whole life, endowment and term assurances, annuities, unit-linked contracts, and unitised with-profits contracts, incorporating multiple decrement models as appropriate.
3. Profit test simple annual premium contracts of the types listed in 2. and determine the profit vector, the profit signature, the net present value, and the profit margin.
4. Show how a profit test may be used to price a product, and use a profit test to calculate a premium for a conventional (without profits) life insurance contract.
5. Show how, for unit-linked contracts, non-unit reserves can be established to eliminate future negative cash flows, using a profit test model.
(v) Describe the principal forms of heterogeneity within a population and the ways in which selection can occur.
1. Explain why it is necessary to have different mortality tables for different classes of lives.
2. Explain the theoretical basis of the use of risk classification in life insurance.
3. State the principal factors which contribute to the variation in mortality and morbidity by region and according to the social and economic environment, specifically:
* occupation
* nutrition
* housing
* climate/geography
* education
* genetics
4. Define and give examples of the main forms of selection:
* temporary initial selection
* class selection
* time selection
* spurious selection
* adverse selection
5. Explain how selection can be expected to occur amongst individuals or groups taking out each of the main types of life insurance contracts, or amongst members of large pension schemes.
6. Explain the concept of mortality convergence
7. Explain how decrements can have a selective effect.
8. Explain the concept of a single figure index and its advantages and disadvantages for summarising and comparing actual experience.
9. Define the terms crude mortality rate, directly standardised and indirectly standardised mortality rate, standardised mortality ratio, and illustrate their use.
Teaching will be delivered in a way that blends face-to-face classes, for those students that can be present on campus, with a range of online lectures, teaching, learning and collaborative support.
This module does not appear to have a published bibliography for this year.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Coursework |
Test |
|
|
| Exam |
Main exam: 120 minutes during Summer (Main 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.
Your department will provide further guidance before your exams.
Overall assessment
Reassessment
Module supervisor and teaching staff
Dr Jackie Wong Siaw Tze, email: jw19203@essex.ac.uk.
Dr Jackie Wong
jw19203@essex.ac.uk
No
No
No
Dr Dimitrina Dimitrova
Cass Business School, City, University of London
Senior Lecturer
Available via Moodle
Of 1409 hours, 30 (2.1%) hours available to students:
1379 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
Disclaimer: The University makes every effort to ensure that this information on its Module Directory is accurate and up-to-date. Exceptionally it can
be necessary to make changes, for example to programmes, modules, facilities or fees. Examples of such reasons might include a change of law or regulatory requirements,
industrial action, lack of demand, departure of key personnel, change in government policy, or withdrawal/reduction of funding. Changes to modules may for example consist
of variations to the content and method of delivery or assessment of modules and other services, to discontinue modules and other services and to merge or combine modules.
The University will endeavour to keep such changes to a minimum, and will also keep students informed appropriately by updating our programme specifications and module directory.
The full Procedures, Rules and Regulations of the University governing how it operates are set out in the Charter, Statutes and Ordinances and in the University Regulations, Policy and Procedures.