Table of Contents
Introduction
What Is a 3D Array — Really?
Real-World Scenario: Predicting Claim Severity by Region, Product, and Time
How to Build and Use a 3D Risk Matrix
Complete Implementation with Test Cases
Best Practices and Performance Tips
Conclusion
Introduction
Most developers think 3D arrays are for game engines or scientific simulations.
They’re wrong.
In insurance, 3D arrays are the secret weapon behind AI-driven pricing — quietly powering models that predict who will claim, what they’ll claim for, and when it’ll happen.
This isn’t theory. It’s how top insurers cut losses by 22% without raising premiums.
In this article, you’ll learn how to use a 3D array to map claim severity across regions, policy types, and months — all in clean, production-ready Python.
No ML libraries. No black boxes. Just math, logic, and one powerful data structure.
What Is a 3D Array — Really?
A 3D array is a list of lists of lists.
Think of it as a cube of data:
X-axis: Geographic regions (e.g., North, South, East, West)
Y-axis: Policy types (e.g., Auto, Home, Health)
Z-axis: Time periods (e.g., Jan 2024, Feb 2024, …)
Each cell holds a value: average claim severity.
This structure lets you answer questions like:
“In the South, how much do home claims cost in winter?”
“Is auto claim severity rising faster in the East than the West?”
It’s not just storage — it’s context-aware analytics.
Real-World Scenario: Predicting Claim Severity by Region, Product, and Time
Let's say you’re at a national insurer.
You have 3 years of claims data. You need to adjust pricing before the next hurricane season.
Your goal:
Build a 3D risk matrix that shows average claim cost per region, per policy type, per month.
You don’t need a data warehouse. You just need a 3D array — and the discipline to fill it right.
How to Build and Use a 3D Risk Matrix
1. Initialize with Zeroes (Safe & Clear)
regions = ["North", "South", "East", "West"]
products = ["Auto", "Home", "Health"]
months = list(range(1, 13)) # Jan to Dec
# 3D array: [region][product][month] → claim severity
risk_matrix = [
[[0.0 for _ in months] for _ in products]
for _ in regions
]
Never use [[[0]*len(months)]*len(products)]*len(regions) — that creates shared references. This is the only safe way.
2. Populate with Real Data
# Simulated data: (region_idx, product_idx, month_idx, severity)
claims_data = [
(0, 0, 2, 1800), # North, Auto, Mar, $1800
(1, 1, 7, 4200), # South, Home, Aug, $4200
(2, 2, 1, 2900), # East, Health, Jan, $2900
(3, 0, 11, 2100), # West, Auto, Dec, $2100
# ... hundreds more
]
for r, p, m, severity in claims_data:
risk_matrix[r][p][m-1] += severity # m-1 because months are 1-indexed in data
3. Compute Averages with Zero-Safety
from collections import defaultdict
claim_counts = [
[[0 for _ in months] for _ in products]
for _ in regions
]
# Count claims per cell
for r, p, m, _ in claims_data:
claim_counts[r][p][m-1] += 1
# Compute average severity
for r in range(len(regions)):
for p in range(len(products)):
for m in range(len(months)):
if claim_counts[r][p][m] > 0:
risk_matrix[r][p][m] /= claim_counts[r][p][m]
Always divide by count — never assume data exists.
4. Query Like a Pro
def get_severity(risk_matrix, region, product, month):
r_idx = regions.index(region)
p_idx = products.index(product)
m_idx = month - 1 # Convert 1-based month to 0-based index
return risk_matrix[r_idx][p_idx][m_idx]
# Example: How much do home claims cost in the South in July?
avg_home_claim_july = get_severity(risk_matrix, "South", "Home", 7)
print(f"Average home claim in South (July): ${avg_home_claim_july:,.0f}")
Complete Implementation with Test Cases
from typing import List, Tuple
import unittest
class InsuranceRiskMatrix:
def __init__(self, regions: List[str], products: List[str], months: List[int]):
self.regions = regions
self.products = products
self.months = months
n, p, m = len(regions), len(products), len(months)
# Safe 3D initialization
self.matrix = [[[0.0 for _ in range(m)] for _ in range(p)] for _ in range(n)]
self.counts = [[[0 for _ in range(m)] for _ in range(p)] for _ in range(n)]
def add_claim(self, region: str, product: str, month: int, severity: float):
r = self.regions.index(region)
p = self.products.index(product)
m = month - 1 # Convert to 0-based
if m < 0 or m >= len(self.months):
raise ValueError(f"Invalid month: {month}")
self.matrix[r][p][m] += severity
self.counts[r][p][m] += 1
def get_average_severity(self, region: str, product: str, month: int) -> float:
r = self.regions.index(region)
p = self.products.index(product)
m = month - 1
if self.counts[r][p][m] == 0:
return 0.0
return self.matrix[r][p][m] / self.counts[r][p][m]
def get_high_risk_months(self, region: str, product: str, threshold: float) -> List[int]:
r = self.regions.index(region)
p = self.products.index(product)
high_risk = []
for m_idx, m in enumerate(self.months):
avg = self.get_average_severity(region, product, m)
if avg > threshold:
high_risk.append(m)
return high_risk
class TestInsuranceRiskMatrix(unittest.TestCase):
def setUp(self):
self.regions = ["North", "South", "East", "West"]
self.products = ["Auto", "Home", "Health"]
self.months = list(range(1, 13))
self.matrix = InsuranceRiskMatrix(self.regions, self.products, self.months)
# Simulate claims data
claims = [
("North", "Auto", 3, 1800),
("South", "Home", 7, 4200),
("East", "Health", 1, 2900),
("West", "Auto", 12, 2100),
("South", "Home", 7, 4500), # Duplicate month, same product
("North", "Auto", 3, 1900),
]
for r, p, m, s in claims:
self.matrix.add_claim(r, p, m, s)
def test_add_and_retrieve(self):
avg = self.matrix.get_average_severity("South", "Home", 7)
self.assertAlmostEqual(avg, 4350.0, places=1) # (4200 + 4500) / 2
def test_zero_count_returns_zero(self):
avg = self.matrix.get_average_severity("East", "Auto", 5)
self.assertEqual(avg, 0.0)
def test_high_risk_months(self):
high_risk = self.matrix.get_high_risk_months("South", "Home", 4000)
self.assertEqual(high_risk, [7])
def test_edge_cases(self):
with self.assertRaises(ValueError):
self.matrix.add_claim("North", "Auto", 15, 1000) # Invalid month
with self.assertRaises(ValueError):
self.matrix.get_average_severity("Central", "Home", 6) # Invalid region
if __name__ == "__main__":
# Demo
regions = ["North", "South", "East", "West"]
products = ["Auto", "Home", "Health"]
months = list(range(1, 13))
insurer = InsuranceRiskMatrix(regions, products, months)
# Simulate real claims
sample_claims = [
("North", "Auto", 1, 1200), ("North", "Auto", 2, 1400),
("South", "Home", 7, 4100), ("South", "Home", 8, 4300),
("East", "Health", 1, 2800), ("West", "Auto", 12, 2200),
("South", "Home", 7, 4500), ("North", "Auto", 1, 1100),
]
for region, product, month, severity in sample_claims:
insurer.add_claim(region, product, month, severity)
print(" INSURANCE RISK MATRIX: CLAIM SEVERITY ANALYSIS")
print(f"{'Region':<8} {'Product':<8} {'Month':<6} {'Avg Claim':<12}")
print("-" * 50)
for r in regions:
for p in products:
for m in months:
avg = insurer.get_average_severity(r, p, m)
if avg > 0:
print(f"{r:<8} {p:<8} {m:<6} ${avg:,.0f}")
print("\n High-risk months for Home in South:")
high_risk = insurer.get_high_risk_months("South", "Home", 4000)
print(f"Months: {high_risk} — Time to adjust premiums!")
print("\n Running tests...")
unittest.main(argv=[''], exit=False, verbosity=1)
Best Practices and Performance Tips
Always initialize 3D arrays with nested comprehensions — never use * multiplication.
Track counts separately — avoids division by zero and lets you update incrementally.
Use enums or constants for regions/products — regions[0] is a bug waiting to happen.
Validate inputs — invalid months or regions break everything.
Use this for static or semi-static data — if data changes hourly, use a database.
Export to JSON or CSV for reporting: json.dumps(risk_matrix) works perfectly.
Conclusion
3D arrays aren’t for physicists.
They’re for insurance underwriters, risk analysts, and fintech engineers who need to answer:
“Where is risk rising — and why?”
You don’t need TensorFlow to predict claims. You just need a cube of data — and the discipline to fill it right. Master this, and you’re not writing code. You’re building the invisible engine that keeps insurers profitable.
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