Principles of Actuarial Modelling
This domain tests how actuaries choose, build, calibrate, validate and communicate models, and how they allow for uncertainty in projections.
Model principles
- A model is a simplified representation of reality. It should be fit for purpose, parsimonious, transparent and consistent with the data and actuarial theory.
- Deterministic models produce single-point projections. Stochastic models produce distributions, often using Monte Carlo simulation. State models such as alive/dead or healthy/sick are common in actuarial work.
- Calibration estimates parameters from data. Validation checks whether the model reproduces known features and performs out of sample. Sensitivity and scenario testing show how results respond to changes in assumptions.
- Model risk arises from wrong structure, parameter error, data error and implementation error. Parameter uncertainty and correlation between assumptions should not be ignored.
Worked example
A simple two-state alive/dead model has 1,000 lives aged x and an annual mortality probability q_x = 0.02. The expected number alive after two years is 1,000 x (1 - 0.02)^2 = 960.4. A deterministic projection reports 960.4 lives. A stochastic simulation would also report the distribution of the number alive, showing the range around that mean. If the model ignores improvement in mortality, the projection will systematically overstate deaths in later years.
Traps that cost marks
Do not present a model output as certainty. Do not overfit a model to historical data so that it fails to generalise. Do not confuse a scenario with a sensitivity: a scenario is a coherent alternative future, while a sensitivity changes one assumption at a time. Always state the purpose and limitations of the model.