Actuarial Math, Visualized

Short mathematical animations that explain how actuarial models work and why their assumptions matter.

Episode 01: Lee-Carter mortality forecasting

Watch the 42.8-second video — 1080 × 1350, 30 fps.

The first video follows the complete Lee-Carter idea in under one minute:

1. mortality rates form an age-by-year surface;
2. a_x describes the average mortality pattern by age;
3. b_x measures how strongly each age reacts to the time trend;
4. forecasting k_t produces a future mortality curve;
5. those projections feed survival and annuity calculations.

The scene fits the model with singular value decomposition. It uses a deterministic, illustrative mortality surface so the repository remains self-contained and does not redistribute licensed Human Mortality Database data.

The model is

log m(x,t) = a(x) + b(x) k(t) + epsilon(x,t)

with the usual identification constraints sum(b_x) = 1 and mean(k_t) = 0.

Render locally

Requirements: Python 3.11+ and FFmpeg.

py -3.11 -m venv .venv
.\.venv\Scripts\python.exe -m pip install --upgrade pip
.\.venv\Scripts\python.exe -m pip install -e ".[dev]"
.\.venv\Scripts\python.exe -m pytest
.\.venv\Scripts\python.exe -m manim --config_file manim.cfg `
  src\actuarial_math_visualized\scene.py LeeCarterVisualized

The final social-media render is copied to assets/lee-carter-visualized.mp4.

Project map

src/actuarial_math_visualized/model.py  Lee-Carter fit and forecast
src/actuarial_math_visualized/scene.py  4:5 Manim animation
tests/test_model.py                     numerical contract tests
assets/                                 final video and thumbnail

Created by Amine Manai. MIT licensed.