Risk Premium (Variance Load)

This pricing rule starts with the expected claim cost and then adds an extra amount that grows with the spread of possible losses. The variance term matters because two risks can have the same average loss but very different uncertainty; the one with more volatile outcomes is more dangerous to the insurer, so it deserves a higher premium. The parameter θ controls how strongly uncertainty is penalized, with larger values producing more conservative pricing.

Use this formula when pricing insurance or risk-transfer contracts where both average loss and loss volatility are relevant, especially in simple actuarial models or risk-loading frameworks. It is most useful when you want a mathematically transparent premium that increases as claim variability increases.

• Using standard deviation instead of variance in the loading term
• Forgetting that θ multiplies Var(X) before adding it to the expected loss
• Treating θ as a fixed constant across all products without checking whether the model assumes different risk appetites