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: altair 6.1.0 | Python 3.13.13
Quality: 89/100 | Updated: 2026-06-03
"""
import os
import sys as _sys
# Prevent this file from shadowing the installed altair package.
# Python inserts the script's directory as sys.path[0] when running `python altair.py`.
_self_dir = os.path.dirname(os.path.abspath(__file__))
if _self_dir in _sys.path:
_sys.path.remove(_self_dir)
del _sys, _self_dir
import altair as alt
import numpy as np
import pandas as pd
from PIL import Image
# Theme-adaptive chrome (Imprint palette)
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
# Canvas — square 2400×2400 for symmetric heatmap grid
TW, TH = 2400, 2400
# Imprint sequential colormap: brand green → blue (single-polarity, claim magnitude)
IMPRINT_SEQ_START = "#009E73" # Imprint palette position 1
IMPRINT_SEQ_END = "#4467A3" # Imprint palette position 3
AMBER = "#DDCC77" # Imprint amber — IBNR boundary marker
# Data — cumulative paid claims triangle (10 accident years × 10 development periods)
np.random.seed(42)
accident_years = list(range(2015, 2025))
dev_periods = list(range(1, 11))
n_years = len(accident_years)
base_claims = np.array([3200, 3500, 3800, 4100, 3900, 4300, 4600, 4200, 4800, 5100]) * 1000
dev_factors = [2.50, 1.45, 1.22, 1.12, 1.07, 1.04, 1.025, 1.015, 1.008]
cumulative = np.zeros((n_years, len(dev_periods)))
for i in range(n_years):
cumulative[i, 0] = base_claims[i] + np.random.normal(0, base_claims[i] * 0.05)
for j in range(1, len(dev_periods)):
noise = 1 + np.random.normal(0, 0.01)
cumulative[i, j] = cumulative[i, j - 1] * dev_factors[j - 1] * noise
rows = []
for i, year in enumerate(accident_years):
for j, period in enumerate(dev_periods):
is_projected = (i + j) >= n_years
amount = round(cumulative[i, j])
label = f"{amount / 1e6:.1f}M" if amount >= 1e6 else f"{amount / 1e3:.0f}K"
rows.append(
{
"Accident Year": str(year),
"Development Period": period,
"Cumulative Amount": amount,
"Status": "Projected (IBNR)" if is_projected else "Actual",
"Label": label,
}
)
df = pd.DataFrame(rows)
legend_data = pd.DataFrame(
[{"legend_label": "Actual (Observed)", "legend_order": 0}, {"legend_label": "Projected (IBNR)", "legend_order": 1}]
)
factor_rows = []
for j, factor in enumerate(dev_factors):
factor_rows.append({"Accident Year": "Dev Factor", "Development Period": j + 1, "Factor": f"{factor:.3f}"})
df_factors = pd.DataFrame(factor_rows)
year_order = [str(y) for y in accident_years] + ["Dev Factor"]
min_val = df["Cumulative Amount"].min()
max_val = df["Cumulative Amount"].max()
x_enc = alt.X(
"Development Period:O",
axis=alt.Axis(labelFontSize=10, titleFontSize=12, labelAngle=0, orient="top", titlePadding=10),
)
y_enc = alt.Y(
"Accident Year:N",
sort=[str(y) for y in accident_years],
axis=alt.Axis(labelFontSize=10, titleFontSize=12, titlePadding=10),
)
# Heatmap cells with Imprint sequential colormap encoding cumulative claim magnitude
heatmap = (
alt.Chart(df)
.mark_rect(stroke=PAGE_BG, strokeWidth=1.5, cornerRadius=1)
.encode(
x=x_enc,
y=y_enc,
color=alt.Color(
"Cumulative Amount:Q",
scale=alt.Scale(range=[IMPRINT_SEQ_START, IMPRINT_SEQ_END], domain=[min_val, max_val]),
legend=alt.Legend(
title="Cumulative Claims",
titleFontSize=10,
labelFontSize=10,
gradientLength=200,
gradientThickness=12,
orient="right",
offset=12,
),
),
opacity=alt.when(alt.datum.Status == "Actual").then(alt.value(1.0)).otherwise(alt.value(0.6)),
tooltip=[
alt.Tooltip("Accident Year:N"),
alt.Tooltip("Development Period:O"),
alt.Tooltip("Cumulative Amount:Q", format=",.0f", title="Cumulative ($)"),
alt.Tooltip("Status:N"),
],
)
)
# Dashed amber border on projected cells — marks the IBNR evaluation boundary
projected_df = df[df["Status"] == "Projected (IBNR)"].copy()
projected_border = (
alt.Chart(projected_df)
.mark_rect(stroke=AMBER, strokeWidth=2.5, strokeDash=[6, 3], filled=False, cornerRadius=1)
.encode(x=x_enc, y=y_enc)
)
# Cell text annotations — ink color adapts for contrast over light/dark cells
text = (
alt.Chart(df)
.mark_text(fontSize=12, fontWeight="bold")
.encode(
x=x_enc,
y=y_enc,
text="Label:N",
color=alt.when(alt.datum["Cumulative Amount"] > (max_val * 0.55))
.then(alt.value(PAGE_BG))
.otherwise(alt.value(INK)),
)
)
# Dev factors background row (age-to-age chain-ladder factors)
factor_bg = (
alt.Chart(df_factors)
.mark_rect(fill=ELEVATED_BG, stroke=INK_SOFT, strokeWidth=1, cornerRadius=1)
.encode(x=alt.X("Development Period:O"), y=alt.Y("Accident Year:N", sort=year_order))
)
factor_text = (
alt.Chart(df_factors)
.mark_text(fontSize=11, fontWeight="bold", color=INK_SOFT)
.encode(x=alt.X("Development Period:O"), y=alt.Y("Accident Year:N", sort=year_order), text="Factor:N")
)
# Status legend placed at bottom to avoid crowding the right-side color legend
status_legend = (
alt.Chart(legend_data)
.mark_square(size=150, stroke=INK_SOFT, strokeWidth=1)
.encode(
opacity=alt.Opacity(
"legend_label:N",
scale=alt.Scale(domain=["Actual (Observed)", "Projected (IBNR)"], range=[1.0, 0.6]),
legend=alt.Legend(
title="Status",
titleFontSize=10,
labelFontSize=10,
orient="bottom",
offset=12,
symbolType="square",
symbolSize=150,
symbolStrokeWidth=1.5,
symbolFillColor=IMPRINT_SEQ_START,
),
)
)
)
chart = (
(heatmap + projected_border + text + factor_bg + factor_text + status_legend)
.properties(
width=360,
height=380,
background=PAGE_BG,
title=alt.Title(
"heatmap-loss-triangle · python · altair · anyplot.ai",
subtitle=[
"Cumulative paid claims development triangle with chain-ladder projections.",
"Full opacity = actual observed | Faded + dashed border = projected (IBNR) | Bottom row = age-to-age factors.",
],
fontSize=16,
subtitleFontSize=11,
subtitleColor=INK_MUTED,
color=INK,
anchor="start",
offset=12,
),
padding={"left": 20, "right": 20, "top": 20, "bottom": 20},
)
.configure_axis(grid=False, domainWidth=0, labelColor=INK_SOFT, titleColor=INK, tickColor=INK_SOFT)
.configure_view(strokeWidth=0, fill=PAGE_BG)
.configure_legend(fillColor=ELEVATED_BG, strokeColor=INK_SOFT, labelColor=INK_SOFT, titleColor=INK)
.configure_title(color=INK)
)
# Save PNG then pad to exact 2400×2400 target (square format for symmetric heatmap)
chart.save(f"plot-{THEME}.png", scale_factor=4.0)
chart.save(f"plot-{THEME}.html")
_img = Image.open(f"plot-{THEME}.png").convert("RGB")
_w, _h = _img.size
if _w > TW or _h > TH:
raise SystemExit(
f"altair vl-convert produced {_w}×{_h}, exceeds target {TW}×{TH}. "
f"Shrink chart .properties(width=, height=) values and re-render."
)
if _w < TW or _h < TH:
_canvas = Image.new("RGB", (TW, TH), PAGE_BG)
_canvas.paste(_img, ((TW - _w) // 2, (TH - _h) // 2))
_canvas.save(f"plot-{THEME}.png")
Part of Actuarial Loss Development Triangle on anyplot.ai.