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: letsplot 4.10.1 | Python 3.13.13
Quality: 86/100 | Updated: 2026-06-03
"""
import os
import numpy as np
import pandas as pd
from lets_plot import *
LetsPlot.setup_html()
# Theme tokens (Imprint palette — theme-adaptive chrome)
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"
ANYPLOT_AMBER = "#DDCC77" # warning / caution anchor — outside the categorical pool
# 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)
n_periods = len(dev_periods)
# Age-to-age development factors (realistic chain-ladder factors)
age_to_age_factors = [2.50, 1.45, 1.22, 1.12, 1.07, 1.04, 1.025, 1.015, 1.008]
# Generate realistic initial claims and build cumulative triangle
initial_claims = np.random.uniform(8000, 15000, n_years)
triangle = np.full((n_years, n_periods), np.nan)
for i in range(n_years):
triangle[i, 0] = initial_claims[i]
for j in range(1, n_periods):
noise = max(np.random.normal(1.0, 0.02), 1.0 / age_to_age_factors[j - 1])
triangle[i, j] = triangle[i, j - 1] * age_to_age_factors[j - 1] * noise
# Build main heatmap dataframe
rows = []
for i in range(n_years):
for j in range(n_periods):
is_projected = (i + j) >= n_years
rows.append(
{
"accident_year": str(accident_years[i]),
"dev_period": str(dev_periods[j]),
"cumulative": triangle[i, j],
"region": "Projected" if is_projected else "Actual",
}
)
df = pd.DataFrame(rows)
df["label"] = df["cumulative"].apply(lambda v: f"{v:,.0f}")
# Text color: white on dark cells, INK on lighter cells (contrast against fill gradient)
max_val = df["cumulative"].max()
min_val = df["cumulative"].min()
df["text_color"] = df["cumulative"].apply(lambda v: "white" if (v - min_val) / (max_val - min_val) > 0.55 else INK)
# Build development factors row (9 factors + terminal "—")
factor_rows = []
for j in range(len(age_to_age_factors)):
factor_rows.append(
{"accident_year": "Factor", "dev_period": str(dev_periods[j]), "label": f"{age_to_age_factors[j]:.3f}"}
)
factor_rows.append({"accident_year": "Factor", "dev_period": str(dev_periods[-1]), "label": "—"})
df_factors = pd.DataFrame(factor_rows)
# Y-axis ordering: Factor at bottom, 2024 above, 2015 at top
y_order = ["Factor"] + [str(y) for y in reversed(accident_years)]
# Separate actual and projected
df_actual = df[df["region"] == "Actual"].copy()
df_projected = df[df["region"] == "Projected"].copy()
# Invisible points for Actual/Projected legend (lets-plot guide trick)
df_legend = pd.DataFrame(
{
"x": [str(dev_periods[0]), str(dev_periods[0])],
"y": [str(accident_years[0]), str(accident_years[0])],
"region": ["Actual", "Projected"],
}
)
# Split cell annotations by text color for contrast against fill gradient
df_light_text = df[df["text_color"] == "white"].copy()
df_dark_text = df[df["text_color"] != "white"].copy()
# Focal point: identify peak projected (IBNR) cell for storytelling annotation
max_proj_idx = df_projected["cumulative"].idxmax()
max_proj_row = df_projected.loc[max_proj_idx]
df_peak = pd.DataFrame(
{
"accident_year": [max_proj_row["accident_year"]],
"dev_period": [max_proj_row["dev_period"]],
"text": [f"Peak IBNR\n${max_proj_row['cumulative']:,.0f}"],
}
)
title = "heatmap-loss-triangle · python · letsplot · anyplot.ai"
# Theme-adaptive chrome
anyplot_theme = theme(
plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
panel_background=element_rect(fill=PAGE_BG),
panel_grid=element_blank(),
panel_border=element_blank(),
axis_line=element_blank(),
axis_ticks=element_blank(),
axis_title=element_text(color=INK, size=14, face="bold"),
axis_text=element_text(color=INK_SOFT, size=12),
plot_title=element_text(color=INK, size=16, face="bold"),
plot_subtitle=element_text(color=INK_SOFT, size=12, face="italic"),
plot_caption=element_text(color=INK_MUTED, size=11),
legend_background=element_rect(fill=ELEVATED_BG, color=INK_SOFT),
legend_text=element_text(color=INK_SOFT, size=13),
legend_title=element_text(color=INK, size=15, face="bold"),
legend_position="right",
plot_margin=[30, 20, 20, 20],
)
# Base flavor: lets-plot exclusive dark theme for dark renders
base_flavor = flavor_darcula() if THEME == "dark" else theme_minimal()
# Plot
plot = (
ggplot()
# Actual cells: border in INK_SOFT (theme-adaptive grey)
+ geom_tile(aes(x="dev_period", y="accident_year", fill="cumulative"), data=df_actual, color=INK_SOFT, size=1.0)
# Projected cells: amber border + slightly reduced alpha marks the IBNR region
+ geom_tile(
aes(x="dev_period", y="accident_year", fill="cumulative"),
data=df_projected,
color=ANYPLOT_AMBER,
size=1.4,
alpha=0.75,
)
# Cell annotations — split by text color for readability across gradient
+ geom_text(aes(x="dev_period", y="accident_year", label="label"), data=df_light_text, color="white", size=4.5)
+ geom_text(aes(x="dev_period", y="accident_year", label="label"), data=df_dark_text, color=INK, size=4.5)
# Invisible points for Actual / Projected legend via guide_legend override_aes
+ geom_point(aes(x="x", y="y", color="region"), data=df_legend, size=0, alpha=0)
+ scale_color_manual(
values={"Actual": INK_SOFT, "Projected": ANYPLOT_AMBER},
name="Cell Region",
guide=guide_legend(override_aes={"size": 8, "alpha": 1, "shape": 15}),
)
# Factor row tiles with elevated background
+ geom_tile(aes(x="dev_period", y="accident_year"), data=df_factors, fill=ELEVATED_BG, color=INK_SOFT, size=0.8)
# Factor labels in bold
+ geom_text(
aes(x="dev_period", y="accident_year", label="label"), data=df_factors, color=INK, size=4.0, fontface="bold"
)
# Focal point: callout on peak projected (IBNR) cell for data storytelling
+ geom_text(
aes(x="dev_period", y="accident_year", label="text"),
data=df_peak,
color=ANYPLOT_AMBER,
size=3.8,
fontface="bold",
)
# Imprint sequential colormap: brand green → blue (single-polarity magnitude)
+ scale_fill_gradient(low="#009E73", high="#4467A3", name="Cumulative\nClaims ($)")
+ scale_x_discrete(limits=[str(p) for p in dev_periods])
+ scale_y_discrete(limits=y_order)
+ labs(
x="Development Period (Years)",
y="Accident / Origin Year",
title=title,
subtitle="Chain-Ladder Loss Triangle · Actual (grey border) vs Projected (amber border)",
caption="Bottom row: Age-to-Age Development Factors",
)
+ ggsize(600, 600)
+ base_flavor
+ anyplot_theme
)
# Save
ggsave(plot, f"plot-{THEME}.png", path=".", scale=4)
ggsave(plot, f"plot-{THEME}.html", path=".")
Part of Actuarial Loss Development Triangle on anyplot.ai.