Prerequisite Knowledge
Summary of the prerequisite knowledge assumed in this subject.
To view the formal eligibility and requirements — prerequisites, corequisites, recommended background knowledge and core participation requirements — please see the University Handbook (ACTL20004, ACTL90021). The lists below are a practical, topic-level companion: the specific mathematical, statistical and Excel skills we assume you already have, and where in the subject each one is used.
Topics are grouped by how much a gap will cost you:
- Critical — used repeatedly and not taught from scratch anywhere; a gap here can block whole exercise sets.
- Important — a gap typically costs you a question or two rather than a module.
- Background — assumed, but rarely the thing that blocks you; most are already covered by the subjects listed as prerequisites in the Handbook.
The Modules column shows where each topic is used, so you can see it in context. If you would like to check where you stand before the subject starts, the Readiness Diagnostic agent will walk you through these topics and tell you where to review.
1 Mathematics and statistics
1.1 Critical
| Topic | What you should be able to do | Modules |
|---|---|---|
| Moment generating functions | The definition \(M_X(r)=\mathrm{E}(e^{rX})\) and how the MGF relates to the moments of \(X\) (you are not expected to memorise the MGFs of particular distributions) | M7–M9 |
| Conditional expectation & law of total variance | \(\mathrm{E}(S)=\mathrm{E}\big(\mathrm{E}(S\mid N)\big)\) and \(\mathrm{Var}(S)=\mathrm{E}\big(\mathrm{Var}(S\mid N)\big)+\mathrm{Var}\big(\mathrm{E}(S\mid N)\big)\); working with conditional models | M2, M7 |
| Expectation algebra for independent sums and products | \(\mathrm{E}\!\left[\prod_t (1+i_t)\right]=\prod_t \mathrm{E}[1+i_t]\); the variance of a product; \(\mathrm{E}[X^2]=\mathrm{Var}(X)+\mathrm{E}[X]^2\); when independence lets you factorise and when it does not | M10, M11 |
| Statistical inference | Maximum likelihood; what unbiased, minimum-variance and consistent mean; confidence intervals; weighted least squares; fitting and interpreting a linear regression, including log-linear | M2, M12 |
| Normal distribution and \(\Phi\) | Standardising; evaluating and inverting \(\Phi\); reading a z-table by hand; the normal approximation to an aggregate loss | M7, M8, M11 |
Absolute & mixed cell referencing in Excel ($) |
Write one formula that fills a whole triangle by dragging; use F4 to cycle reference types |
M1–M4, M6 |
1.2 Important
| Topic | What you should be able to do | Modules |
|---|---|---|
| Named distributions and their moments | Exponential (including \(\mathrm{E}[X^2]=2\theta^2\)), Poisson, gamma, beta, uniform, Pareto and discrete uniform | M5, M7, M10, M11 |
| Taylor / Maclaurin expansion | Expand a function about a point — both absolute and relative risk aversion are derived this way | M5 |
| Calculus for optimisation | Differentiate, set to zero, check the second-order condition; implicit differentiation | M5, M7, M9 |
| Series and summation | Geometric series, index shifts, double sums | M2, M10 |
| Jensen’s inequality | Recognise when it applies and use it | M2, M10 |
| Transformation of random variables | Find the density of \(g(X)\) by change of variables | M11 |
| Indicator random variables | Set up and use \(\mathbb{1}_{\{\cdot\}}\) | M11, M12 |
| Numerical root-finding | Solve an equation numerically (e.g. a cubic in \(R\), or bounding a root) | M8, M9 |
1.3 Background
Assumed but rarely the blocker — and for the most part already covered by the subjects listed as prerequisites in the Handbook.
| Topic | What you should be able to do | Modules |
|---|---|---|
| Financial mathematics | Accumulation, discounting, present value, annuity-style cash flows, the equivalence principle | M10 |
| Integration | Definite and improper integrals | M5, M8, M9 |
| Descriptive statistics and charting | Summarise and plot data | M6 |
| Coefficient of variation | Definition and use (developed self-contained in the notes) | M10, M11 |
2 Excel
Because everyone has used Excel before, a challenge in this subject is to start at the right level of assumed knowledge. We had to strike a balance between (i) not assuming so much that it is too much work to catch up if you have little experience, and (ii) not assuming so little that no one draws benefit from the subject. Below are the topics we assume as prior knowledge. Numbers correspond to the chapters of Slager and Slager (2020).
It is strongly recommended that you review these topics, including — but not limited to — the “semi-beginner” topics singled out with bullet points.
Ch. 1: Becoming Acquainted with Excel
Ch. 2: Navigating and Working with Worksheets
Ch. 3: Best Ways to Enter and Edit Data
- Autofill: p. 105-116, and p. 298-301
Ch. 4: Formatting and Aligning Data
- Format Painter: 178-181
Ch. 5 Different Ways of Viewing and Printing Your Workbook
Ch. 6 Understanding Backstage
- Freezing rows and columns: 221
Ch. 7 Creating and Using Formulas
Named ranges and constants: 312-332
Absolute and mixed cell references ($): 332-342
Ch. 8: Excel’s Pre-existing Functions
- All important
- New Excel 2019 functions (IFS, MAXIFS, MINIFS): p. 381-398
- Date functions for turning dates into periods (YEAR, MONTH, ROUNDUP): used in the reserving spreadsheets (M2, M3)
- Conditional aggregation (SUMIFS, COUNTIFS, SUMPRODUCT): used in the reserving spreadsheets (M2, M3)
Ch. 9: Auditing, Validating, and Protecting Your Data
- Error Value Messages: p. 432
- Formula Auditing: p. 436-439
Ch. 10: Using Hyperlinks, Combining Text, and Working with the Status Bar
- Concatenation: p. 475-485
Ch. 11: Transferring and Duplicating Data to Other Locations
- Paste special (including with “Transpose”): p. 518-530
Ch. 12: Working with Tables
- Conditional formatting: p.569-581
Ch. 13: Working with Charts
- Sparklines: p. 656-664
Ch. 14: Importing Data