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Chapter 7

Non-Life Insurance Actuarial: Measuring Frequency and Severity

#Ruin Probability#Surplus Process#Stop-Loss Reinsurance#Reinsurance

Non-Life Actuarial Mathematics: Quantifying Uncertain Losses

While life insurance focuses on “when” an event occurs, non-life insurance hinges on “how often (Frequency)” and “how large (Severity)” the losses are. Multiplying these two variables gives us the ‘Total Loss’ we need to predict.

1. Frequency Modeling

The number of accidents that will occur is typically modeled using the Poisson Distribution. It is optimized for representing the count of events occurring within a unit of time.

2. Severity Modeling

The amount of money paid out per accident is often modeled using Lognormal or Pareto distributions. Given the nature of non-life insurance where massive losses occur rarely, handling “Heavy-tailed” distributions is critical.

3. Premium Calculation Process: Pure Premium

The minimum premium a non-life insurer must collect is derived through the following logic:

1
Data Collection

Gather accident statistics and exposure units (e.g., number of cars insured) over the past years.

2
Frequency Analysis

Estimate the average number of accidents per unit.

3
Severity Analysis

Estimate the average insurance benefit paid per accident.

4
Determine Pure Premium

Determine the pure premium by multiplying frequency and severity.

4. Sample Data: Proportion of Total Claims by Size

The chart below shows a typical non-life insurance loss distribution: many small claims and few large-scale events.

Proportion of Total Payouts by Claim Size

While small-scale accidents are overwhelmingly frequent, medium-to-large claims account for a substantial portion of total payouts.


💡 Professor’s Tip

Non-life actuaries must beware of “Black Swans.” While small claims are common, a single large-scale disaster or climate event can trigger losses far beyond historical statistics. This is why designing safety nets like Reinsurance is mandatory.

🔗 Next Step