Fundamentals of Actuarial Mathematics and the Language of Formulas

The introductory block of the Association's actuarial programme for specialists of insurance companies and brokers. The course teaches you to read actuarial mathematics as a professional language: to understand every symbol in a formula, its units of measurement and assumptions, to carry out a calculation on a simple example and to link the result to a premium rate, a reserve or capital. The structure of the block follows the core of the International Actuarial Association education syllabus: probability and statistics, financial mathematics, actuarial models and the professional application of models.

Course programme

1. How to read actuarial mathematics — three rules for reading a formula, accumulation and present value, the life table, aggregate loss.
2. Indices, time, powers and logarithms — the time line, converting rates between payment frequencies, force of interest.
3. Functions, graphs, sums and series — a graph as a logic check, geometric progression and the annuity formula.
4. Interest rates and financial mathematics — i, d, v, δ, nominal and effective rates, annuities-due and annuities-immediate.
5. Derivatives and integrals without formalism — sensitivity to the interest rate, duration, probability as an area.
6. Probability and random variables — Bayes' formula, expectation and variance, value at risk (VaR and TVaR).
7. Distributions and the survival function — Poisson, normal, lognormal, Pareto, event intensity.
8. The life table — l_x, q_x, p_x, survival probability, the value of a death benefit.
9. Frequency, severity and aggregate loss — variance of aggregate loss, two sources of risk, from the risk premium to the premium rate.
10. Matrices, modelling and the Monte Carlo method — regression, generalised linear models, simulation, model governance.
11. Professional judgement, standards and diagnostics — international standards of actuarial practice, glossary of notation, diagnostic problems.

Each lesson comes with notes containing a table of notation, a fully worked example and practice problems, plus a lesson test. At the end there is a 50-question course final test and an ASAB certificate.

Duration: 11 video lessons, 2 h 43 min of video + lesson tests and a final test.