What is behind the premium calculation?
Table of contents
How is the price of insurance actually determined? This seemingly simple question leads directly into the world of insurance mathematics – also known as actuarial science. There, specialists work with probabilities, models, and assumptions to quantify risks and calculate fair, stable premiums.
What does an Actuary do?
An actuary is a mathematically trained expert who specializes in the calculation and assessment of insurance risks. Their task is to answer:
- How likely is a loss?
- What will the average loss be?
- How many insured persons are affected – and when?
- How much money does the company need to set aside today to pay out future benefits?
The Basic Formula of the Premium
Insurance Premium = Expected Loss + Safety Margin + Administrative & Sales Costs – Investment Income
This simplified formula shows:
The premium must not only cover the expected loss but also account for fluctuations (e.g., in natural disasters), costs, and a calculated profit.
Risk & Probability: The Core of Calculation
Insurance is based on risk balancing in large numbers.
This means: Individual losses are unpredictable – but calculable in the mass.
Example:
If statistically 1 out of 1,000 household insurances reports a fire damage of an average of €100,000 per year, the expected loss per contract amounts to €100. This forms the base price – plus surcharges.
Important Assumptions in Premium Calculation:
🔹 Claim Frequency: How often does a damage occur?
🔹 Claim Severity: How expensive is an average loss?
🔹 Contract Duration: How long does the customer stay in the tariff?
🔹 Interest: How does the capital develop in the background?
🔹 Cost Ratio: How high are administration & sales?
Example Calculation (highly simplified):
| Component | Amount |
|---|---|
| Expected Loss | €100 |
| Safety Surcharge | €20 |
| Costs (Sales etc.) | €30 |
| Capital Gains | –€10 |
| Total Premium | €140 per year |
Modern Models & Trends
Today, actuaries use not only traditional tables and probability distributions, but also:
- Stochastic Simulations (e.g., for life insurance)
- Big Data & Machine Learning for individual pricing
- Scenario Analyses for natural disasters & extreme events
- Capital Market Models to assess long-term obligations
Conclusion: Math for Security – and Fairness
Insurance mathematics is more than dry theory: It ensures that insurances remain financially stable, fairly calculated, and future-proof – in the interest of all customers.
Or in other words:
A good insurance requires not only trust – but also reliable mathematics.