In the world of actuarial science, life insurance is often seen as predictable—everyone dies eventually. But Non-Life Insurance Mathematics (also known as General Insurance) is the wild west of the industry. It covers everything from a cracked smartphone screen to a massive hurricane hitting a coastal city. This unit is the study of “short-term” risks where the timing is random and the cost is even more uncertain. For students, it is a rigorous challenge that combines heavy-duty probability distributions with the practical reality of corporate solvency.
Below is the exam paper download link
PDF Past Paper On Non-Life Insurance Mathematics For Revision
Above is the exam paper download link
To help you master the pricing and reserving of these unpredictable risks, we have distilled the core examination hurdles into this sharp Q&A revision guide.
What is the primary focus of Non-Life Insurance Mathematics?
Unlike life insurance, which deals with mortality, non-life insurance focuses on Frequency (how often do accidents happen?) and Severity (how much does each accident cost?). The goal is to build a mathematical model that predicts the “Total Claim Amount” for a portfolio so the company can set premiums that are high enough to pay claims but low enough to stay competitive.
How do we model ‘Claim Frequency’?
The most common tool for frequency is the Poisson Distribution. It assumes that claims occur independently and at a constant rate. However, if the data shows that claims are “clumpy” (more variance than the mean), we shift to the Negative Binomial Distribution. In an exam, you will often be asked to justify which distribution fits a specific set of historical data.
What are ‘Severity Models’ and why is the ‘Pareto’ Distribution so important?
Severity models describe the size of a single loss. While many things in nature follow a Normal distribution, insurance claims do not. They have “Heavy Tails.” The Pareto Distribution is the favorite of examiners because it accounts for the “Top 1%” of claims—the catastrophic fires or massive lawsuits—that can wipe out an insurer’s profit. Mastering the “Mean Excess Function” of these distributions is a key skill for advanced papers.
What is the ‘Aggregate Claim Amount’ ($S$)?
This is the “Big Boss” of non-life math. It is the sum of a random number of random variables:
Where $N$ is the frequency and $X$ is the severity. Because $N$ is random, $S$ is a Compound Distribution. You will need to be comfortable using the Panjer Recursion or the Fast Fourier Transform to calculate the probability distribution of $S$ when simple formulas fail.
How do ‘Deductibles’ and ‘Reinsurance’ change the math?
Insurers rarely take 100% of the risk.
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Deductibles: The policyholder pays the first portion of the loss. This “shifts” the severity distribution to the right and reduces the frequency of claims the insurer actually sees.
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Reinsurance: The insurer pays another company to take part of the risk. You must master Excess-of-Loss (where the reinsurer pays the “tail” of a claim) and Proportional (where the risk is shared by percentage) structures.
What is ‘Reserving’ and the ‘Chain Ladder Method’?
A claim might happen today, but it might not be paid for three years (especially in liability insurance). The insurer must set aside money now to pay these Incurred But Not Reported (IBNR) claims. The Chain Ladder Method uses a “Run-off Triangle” of past data to project how much more money will be needed to settle all current claims. If you can’t complete a run-off triangle, you aren’t ready for the final exam!
Conclusion
Non-Life Insurance Mathematics is a discipline of “What Ifs.” It requires a brain that can handle the abstract logic of compound distributions while keeping an eye on the bottom line. Success in your finals comes from your ability to recognize which “Risk Model” fits a specific scenario—whether it’s a fleet of delivery vans or a skyscraper in a flood zone.
To help you practice your IBNR calculations and master the Pareto tail, we have provided a link to the essential PDF revision resource below.
Last updated on: March 25, 2026