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).
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.
