• We are pleased to announce that the winner of our Feedback Prize Draw for the Winter 2024-25 session and winning £150 of gift vouchers is Zhao Liang Tay. Congratulations to Zhao Liang. If you fancy winning £150 worth of gift vouchers (from a major UK store) for the Summer 2025 exam sitting for just a few minutes of your time throughout the session, please see our website at https://www.acted.co.uk/further-info.html?pat=feedback#feedback-prize for more information on how you can make sure your name is included in the draw at the end of the session.
  • Please be advised that the SP1, SP5 and SP7 X1 deadline is the 14th July and not the 17th June as first stated. Please accept out apologies for any confusion caused.

CT5 Proofs

T

TuborgIsBetter

Member
Is the proof of Thiele's equation no longer on the syllabus? Does anybody have a list of proofs that are on the syllabus?
Thanks,
 
The syllabus objective relating to Thiele's equation says that you should "Understand" it.

The proof of Thiele's equation by directly differentiating an expression for the reserve, that used to be in Core Reading, has been removed.

A general reasoning derivation of Thiele's equation based on a short time interval of length dt is still in Core Reading.

As for proofs, then, as for any subject, the exam can test anything that appears in Core Reading. The list below is therefore indicative and not exhaustive, but it does include the types of proofs and bookwork questions that have previously appeared on the CT5 exam:

- expectations and variances of different types of annuities and assurances
- proof that A-bar can be approximated by (i/delta)*A
- manipulation with non-integer age assumptions (constant force of mortality and uniform distribution of deaths)
- proof of premium conversion formulae
- proof that prospective reserve = retrospective reserve
- Thiele’s equation (ie a construction of the equation using the “short time period” method in the notes)
- wordy bookwork on bonus distribution methods
- wordy bookwork on expenses from Chapter 7 (eg definitions, examples)
- proof of formulae linking dependent and independent probabilities
- pension fund commutation factors
- stuff from Chapter 15 (descriptions of selection, statement of formulae for different rates and ratios).
 
so we aren't going to be differentiating anything in line of Thiele's?
 
As I've said, the proof of Thiele's equation by directly differentiating an expression for the reserve is no longer in the Core Reading.
 
Back
Top