A triangular matrix visualization showing cumulative insurance claim payments developing over time. Rows represent accident/origin years, columns represent development periods (e.g., 1-10 years), with the upper-left triangle displaying actual observed cumulative claims and the lower-right triangle showing projected/estimated values (IBNR). This plot is essential for actuarial reserving, enabling analysts to visualize the chain-ladder method and identify development patterns in loss data.
# anyplot.ai
# heatmap-loss-triangle: Actuarial Loss Development Triangle
# Library: makie 0.22.10 | Julia 1.11.9
# Quality: 90/100 | Created: 2026-06-03
using CairoMakie
using Colors
using Random
Random.seed!(42)
# Theme tokens
const THEME = get(ENV, "ANYPLOT_THEME", "light")
const PAGE_BG = THEME == "light" ? colorant"#FAF8F1" : colorant"#1A1A17"
const ELEVATED_BG = THEME == "light" ? colorant"#FFFDF6" : colorant"#242420"
const INK = THEME == "light" ? colorant"#1A1A17" : colorant"#F0EFE8"
const INK_SOFT = THEME == "light" ? colorant"#4A4A44" : colorant"#B8B7B0"
# Approved Imprint colormaps
const ANYPLOT_SEQ = cgrad([colorant"#009E73", colorant"#4467A3"])
const ANYPLOT_DIV = cgrad([colorant"#AE3030", PAGE_BG, colorant"#4467A3"])
# Data: Actuarial loss development triangle
# 10 accident years (2015-2024) x 10 development periods
const N_YEARS = 10
const N_PERIODS = 10
const START_YEAR = 2015
# Ultimate losses per accident year (in $M)
const ULTIMATE = [42.5, 48.2, 51.8, 55.3, 60.1, 63.7, 58.9, 67.4, 72.1, 78.5]
# Age-to-age link ratios (period 1→2, 2→3, ..., 9→10)
const DEV_FACTORS = [3.421, 1.845, 1.412, 1.198, 1.087, 1.042, 1.018, 1.008, 1.003]
# Precompute percent-paid at each development period
pct_at = fill(1.0, N_PERIODS)
for k in (N_PERIODS - 1):-1:1
pct_at[k] = pct_at[k + 1] / DEV_FACTORS[k]
end
# Build the triangle: cumulative amounts at each (year, period) cell
# Year-specific noise only: link ratios then exactly equal DEV_FACTORS (all > 1)
cum_amounts = fill(NaN, N_YEARS, N_PERIODS)
is_projected = fill(false, N_YEARS, N_PERIODS)
yr_noise = [1.0 + randn() * 0.06 for _ in 1:N_YEARS]
for yr in 1:N_YEARS
max_dev = N_YEARS - yr + 1
for dev in 1:N_PERIODS
cum_amounts[yr, dev] = ULTIMATE[yr] * pct_at[dev] * yr_noise[yr]
is_projected[yr, dev] = dev > max_dev
end
end
# Age-to-age factors as weighted average link ratios (sum col k+1 / sum col k)
dev_factor_labels = String[]
for col in 1:(N_PERIODS - 1)
num = 0.0
den = 0.0
for yr in 1:N_YEARS
if !is_projected[yr, col] && !is_projected[yr, col + 1]
num += cum_amounts[yr, col + 1]
den += cum_amounts[yr, col]
end
end
f = den > 0 ? num / den : NaN
push!(dev_factor_labels, isnan(f) ? "—" : string(round(f; digits=3)))
end
# Normalize for colormapping
actual_vals = [cum_amounts[yr, dev]
for yr in 1:N_YEARS for dev in 1:N_PERIODS
if !is_projected[yr, dev] && !isnan(cum_amounts[yr, dev])]
actual_max = maximum(actual_vals)
actual_min = minimum(actual_vals)
proj_vals = [cum_amounts[yr, dev]
for yr in 1:N_YEARS for dev in 1:N_PERIODS
if is_projected[yr, dev] && !isnan(cum_amounts[yr, dev])]
proj_max = isempty(proj_vals) ? 1.0 : maximum(proj_vals)
proj_min = isempty(proj_vals) ? 0.0 : minimum(proj_vals)
# Plot
fig = Figure(
size = (1200, 1200),
fontsize = 13,
backgroundcolor = PAGE_BG,
)
# Title
Label(fig[0, 1],
"Loss Development Triangle · heatmap-loss-triangle · julia · makie · anyplot.ai";
fontsize = 14,
color = INK,
font = :bold,
padding = (0, 0, 12, 0),
tellwidth = false,
)
ax = Axis(
fig[1, 1];
backgroundcolor = PAGE_BG,
titlecolor = INK,
xlabelcolor = INK,
ylabelcolor = INK,
xticklabelcolor = INK_SOFT,
yticklabelcolor = INK_SOFT,
xtickcolor = INK_SOFT,
ytickcolor = INK_SOFT,
leftspinecolor = INK_SOFT,
bottomspinecolor = INK_SOFT,
topspinevisible = false,
rightspinevisible = false,
xgridvisible = false,
ygridvisible = false,
xlabel = "Development Period (Years)",
ylabel = "Accident Year",
xlabelsize = 14,
ylabelsize = 14,
xticklabelsize = 12,
yticklabelsize = 12,
xticks = (1:N_PERIODS, string.(1:N_PERIODS)),
yticks = (1:N_YEARS, string.(START_YEAR:(START_YEAR + N_YEARS - 1))),
yreversed = true,
)
# Draw colored rectangles for each cell
cell_width = 0.92
cell_height = 0.92
for yr in 1:N_YEARS
for dev in 1:N_PERIODS
v = cum_amounts[yr, dev]
projected = is_projected[yr, dev]
isnan(v) && continue
# Determine fill color using approved Imprint colormaps
if projected
t = proj_max > proj_min ? (v - proj_min) / (proj_max - proj_min) : 0.5
fill_color = ANYPLOT_DIV[t * 0.45] # red half only — avoids near-BG midpoint
else
t = actual_max > actual_min ? (v - actual_min) / (actual_max - actual_min) : 0.5
fill_color = ANYPLOT_SEQ[t]
end
poly!(ax,
Point2f[(dev - cell_width / 2, yr - cell_height / 2),
(dev + cell_width / 2, yr - cell_height / 2),
(dev + cell_width / 2, yr + cell_height / 2),
(dev - cell_width / 2, yr + cell_height / 2)];
color = fill_color,
strokecolor = PAGE_BG,
strokewidth = 1.5,
)
# Cell annotation: value in $K with luminance-adaptive text color
m = round(Int, v * 1000)
label_str = m >= 1000 ? string(div(m, 1000), ",", lpad(string(mod(m, 1000)), 3, "0")) : string(m)
lum = 0.299 * red(fill_color) + 0.587 * green(fill_color) + 0.114 * blue(fill_color)
txt_color = lum > 0.45 ? colorant"#1A1A17" : colorant"#F0EFE8"
text!(ax, dev, yr;
text = label_str,
fontsize = 9,
color = txt_color,
align = (:center, :center),
)
end
end
# Diagonal separator line (observed vs projected boundary)
diag_x = Float64[]
diag_y = Float64[]
for yr in 1:(N_YEARS + 1)
max_dev_for_yr = N_YEARS - yr + 2
push!(diag_x, max_dev_for_yr + 0.5)
push!(diag_y, yr - 0.5)
if yr <= N_YEARS
push!(diag_x, max_dev_for_yr + 0.5)
push!(diag_y, yr + 0.5)
end
end
lines!(ax, diag_x, diag_y; color = INK, linewidth = 2.5)
# Development factors row below the main grid
Label(fig[2, 1],
"Age-to-Age Factors: " * join(dev_factor_labels, " → ");
fontsize = 11,
color = INK_SOFT,
tellwidth = false,
padding = (0, 0, 4, 8),
)
# Legend: actual vs projected swatches
Legend(fig[3, 1],
[PolyElement(color = ANYPLOT_SEQ[0.6], strokecolor = :transparent),
PolyElement(color = ANYPLOT_DIV[0.2], strokecolor = :transparent)],
["Actual (observed)", "Projected (IBNR estimate)"];
orientation = :horizontal,
framecolor = ELEVATED_BG,
framevisible = true,
backgroundcolor = ELEVATED_BG,
labelcolor = INK_SOFT,
labelsize = 12,
patchsize = (18, 14),
tellwidth = false,
padding = (8, 8, 6, 6),
)
# Set axis limits
xlims!(ax, 0.5, N_PERIODS + 0.5)
ylims!(ax, 0.5, N_YEARS + 0.5)
# Layout
rowsize!(fig.layout, 0, Auto(0.08))
rowsize!(fig.layout, 1, Auto(1.0))
rowsize!(fig.layout, 2, Auto(0.07))
rowsize!(fig.layout, 3, Auto(0.07))
save("plot-$(THEME).png", fig; px_per_unit = 2)
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/heatmap-loss-triangle/makie/code. Any spec id and library id listed in llms-full.txt fit the same URL shape; every URL below is complete and callable.
{
"spec_id": "heatmap-loss-triangle",
"language": "julia",
"library": "makie",
"page": "https://anyplot.ai/heatmap-loss-triangle/julia/makie",
"hub": "https://anyplot.ai/heatmap-loss-triangle",
"code_json": "https://api.anyplot.ai/specs/heatmap-loss-triangle/makie/code",
"spec_json": "https://api.anyplot.ai/specs/heatmap-loss-triangle",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/heatmap-loss-triangle/julia/makie/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/heatmap-loss-triangle/julia/makie/plot-dark.png",
"quality_score": 90.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Actuarial Loss Development Triangle on anyplot.ai.