Ratemaking And Loss Reserving For Property And Casualty Insurance — Introduction To

The basic formula for calculating the Gross Premium is derived from the Loss Cost (or Pure Premium):

To determine the rate, actuaries calculate the Loss Ratio (Losses / Premium) target and the Expense Ratio (Expenses / Premium) to derive the permissible loss ratio.

The exposure base must be highly correlated with loss potential. The basic formula for calculating the Gross Premium

At its simplest, the pure premium (the portion needed to pay claims and claims-related expenses) is:

Pure Premium = (Expected Losses + Expected LAE) / Number of Exposures To determine the rate, actuaries calculate the Loss

Where exposure is the unit of risk (e.g., car-year for auto, per $100 of payroll for workers’ comp, per $1,000 of property value for homeowners).

The final gross premium includes loading for expenses and profit: To determine the rate

Gross Premium = Pure Premium / (1 – Expense Ratio – Profit & Contingency Load)

Or, using the Loss Ratio Method (more common in commercial lines):

Indicated Loss Ratio = (Projected Losses + LAE) / Projected Earned Premium Indicated Rate Change = (Actual Loss Ratio – Permissible Loss Ratio) / Permissible Loss Ratio

If your permissible loss ratio is 60% (meaning 40% for expenses and profit) and your actual loss ratio is 75%, your indicated rate change is +25%.