ST347-30 Actuarial Methods and Life Contingencies

Introductory description

This module runs in Term 1 and Term 2 and is available for students on a course where it is a listed option and as an Unusual Option to students who have completed the prerequisite modules. It is recommended to take ST338 in parallel with this module.

Results from this module may be partly used to determine exemption eligibility in the Institute and Faculty of Actuaries module CM1. (Independent application with the IFoA may be required to receive the exemption.)

Pre-requisites:
Statistics Students: ST229 Probability for Mathematical Statistics and ST230 Mathematical Statistics.
Non-Statistics Students: ST232 Introduction to Mathematical Statistics or ST233 Introduction to Mathematical Statistics.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Part A Actuarial methods:
Interest rates and discount rates.
Cash flow, equations of value and appraisal.
Perpetuities, Annuities and Loans.
Basic financial instruments.
Bonds, equity and inflation.
Interest rate problems.
Arbitrage and forward contracts.

Part B Life Contingencies:
Simple assurance and annuities, and their evaluation.
Variable benefits and annuities.
Markov chains.
Net premiums and reserves.
Annuities and assurances involving two lives.
Multiple state models, including multiple decrements.
Pensions mathematics.
Cash flow projection techniques.

Learning outcomes

By the end of the module, students should be able to:

• be familiar with basic financial terminology and be able to understand the financial press.
• define the actuarial symbols related to assurance and annuity contracts, understand their interrelationships, and perform relevant calculations.
• understand and use life tables for calculations such as expected values and variances for simple contracts.
• describe and calculate net and gross premiums and premium reserves for various assurance and annuity contracts.
• describe and use methods to estimate cash flows for contracts involving two lives or multiple states, including the use of multiple decrement models.
• describe and use methods for assessing profitability and for pricing contracts.
• explain heterogeneity in populations, and simple methods to deal with heterogeneity.

Indicative reading list

1. Booth, P. (2005) Modern actuarial theory and practice. 2nd ed. Boca Raton, FL: Chapman & Hall/CRC.
2. Faculty of Actuaries in Scotland and Institute of Actuaries (Great Britain) (2002) Formulae
   and tables for examinations of the Faculty of Actuaries and the Institute of Actuaries. [New
   ed.]. [Great Britain]: Faculty of Actuaries and the Institute of Actuaries. Available at:
   https://www.actuaries.org.uk/system/files/field/document/Formulae%20and%20Tables.pdf.
3. Garrett, S. J., McCutcheon, J. J. and Institute and Faculty of Actuaries (Great Britain) (2013)
   An introduction to the mathematics of finance: a deterministic approach. Second edition.
   Kidlington, Oxford: Butterworth-Heinemann is an imprint of Elsevier. Available at:
   https://0-www-sciencedirect-com.pugwash.lib.warwick.ac.uk/science/book/9780080982403.
4. Kellison, S. G. (2009) The theory of interest. 3rd ed. Boston: McGraw-Hill Irwin.
5. Promislow, S. D. (2015) Fundamentals of actuarial mathematics. Third edition. West
   Sussex, England: John Wiley & Sons Ltd. Available at:
   http://ebookcentral.proquest.com/lib/warw/detail.action?docID=1826894.
6. Dickson, D.C., Hardy, M., Hardy, M.R. and Waters, H.R.. Actuarial mathematics for life contingent risks. Cambridge University Press, Second edition (2013).
7. Dickson, D.C., Hardy, M., Hardy, M.R. and Waters, H.R.. Solutions manual for actuarial mathematics for life contingent risks. Cambridge University Press, Second edition (2013).
8. Turnbull, C.. A History of British Actuarial Thought. Palgrave Macmillan (2017).

View reading list on Talis Aspire

Subject specific skills

• Evaluate mathematical and/or statistical techniques.
• Create structured and coherent arguments communicating them in written form.
• Construct and develop logical mathematical arguments with clear identification of assumptions and conclusions.
• Communicate subject-specific information effectively and coherently.
• Evaluate data/problems, including potentially conflicting or incomplete information, abstract essential information and formulate an appropriate analysis/solution strategy using appropriate mathematical language and pursue these strategies through a complete solution cycle.

Transferable skills

• Critical thinking: extracting patterns from incomplete data and using them to form evidence-based conclusions.
• Problem solving: use of logical reasoning to build arguments grounded in evidence and with explicit underlying assumptions.
• Self-awareness: monitoring of your own learning and seeking feedback.
• Communication: verbal discussion of ideas in seminars and among peers; written communication in assignments and the final project.
• Information literacy: evaluation of data and uncertainty in a model-based way.
• Professionalism: self-motivation, taking charge of your own learning, and prioritising effectively.
• Ethics: reflect on professional responsibilities as a statistician in conjunction with the generation and dissemination of information.