Module Directory

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

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.

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.

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.

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.