Insurance calculators
Premium rating
Pure premium from claim frequency and severity, loss trend, fixed and variable expense loadings and profit margin to the gross rate.
Inputs
Results
Pure premium per unit
292.03
Trend factor 1.0816
Gross rate per unit
422.71
Gross premium
4,227,093.33
Expected losses 2,920,320.00
Expected loss ratio
69.1%
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Where each unit of gross rate goes
| Item | Per unit | Share |
|---|---|---|
| Expected losses | 292.03 | 69.1% |
| Fixed expenses | 25.00 | 5.9% |
| Variable expenses | 84.54 | 20.0% |
| Profit | 21.14 | 5.0% |
Methodology
Conventions
- Pure premium = frequency × severity, trended for the years from the experience period to the period the rates will apply.
- Fixed expenses are per unit of exposure. Variable expenses (commission, premium taxes) and the profit margin are shares of the gross premium.
References
- Werner and Modlin, Basic Ratemaking (CAS), ch. 7.
- Klugman, Panjer and Willmot, Loss Models: From Data to Decisions, 5th ed.
Formulas
- Pure premium
- PP = \text{frequency} \times \text{severity} \times (1 + \text{trend})^{t}
- Gross rate
- R = \frac{PP + F}{1 - V - Q}
- Expected loss ratio
- ELR = PP / R