Expected Value of a Claim
Probability-weighted average of possible claim amounts.
Formula
Variables
Example
1% chance of $50,000: E[X] = $500
How it works
The expected value of a claim is the long-run average amount an insurer would expect to pay if the same risk were repeated many times. It is found by multiplying each possible claim amount by the probability of that outcome, then adding those products together. This works because each possible payment contributes to the average in proportion to how often it occurs.
When to use it
Use this when you want to estimate the average cost of an insurance claim from several possible outcomes. It is especially useful in pricing premiums, comparing risks, and assessing whether a policy is likely to be profitable.
Worked example, step by step
Suppose a policy has three possible claim outcomes: - 80% chance of no claim, so x1 = $0 and p1 = 0.80 - 15% chance of a small claim, so x2 = $2,000 and p2 = 0.15 - 5% chance of a large claim, so x3 = $20,000 and p3 = 0.05 Use E[X] = Σ p_i x_i E[X] = (0.80 × 0) + (0.15 × 2000) + (0.05 × 20000) E[X] = 0 + 300 + 1000 E[X] = 1300 Expected value of the claim = $1,300
Common mistakes to avoid
- Forgetting to include the outcome with zero claim amount
- Using percentages like 15 and 5 instead of decimals like 0.15 and 0.05
- Adding the claim amounts without multiplying by their probabilities first
Did You Know?
Insurance works by pooling many small, predictable expected values against rare, ruinous individual losses.
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