Premium Construction — Step by Step
Foundation
The Pure Premium
The pure premium (also called the "loss cost") is the actuarially expected loss per unit of exposure — before any loadings for expenses, profit, or contingency. It answers one question: how much should this risk cost in losses, on average, per year?
Pure premium = Expected Loss Frequency × Expected Loss Severity. For a homeowner's policy: if a home has a 2% probability of filing a claim in any year and the average claim costs $25,000, the pure premium is $500/year ($0.02 × $25,000).
Data Dependency
Pure premium credibility depends directly on the depth of historical loss experience. Personal lines with millions of policies achieve high credibility with 3–5 years of data. Specialty lines may require 10+ years or benchmark industry data to produce stable loss cost estimates.
Development & Trending
Loss Development & Trend Factors
Historical loss data must be adjusted to reflect the future period for which rates will apply. Two adjustments are critical:
Loss development — Reported claims grow over time as late-reported claims emerge and open claims develop to ultimate values. Actuaries apply development factors (derived from loss triangles) to bring historical loss data to estimated ultimate values.
Trend factors — Losses are trended forward to the policy period using historical inflation indices. A loss from 3 years ago must be inflated to reflect current repair costs, medical inflation, litigation trends, and social inflation — the latter now running 6–9% annually in commercial liability lines.
"Social inflation — the rising cost of litigation, jury verdicts, and legal system abuse — is the most significant unmodelled risk in liability pricing today."
— Swiss Re Institute, Casualty Report 2025
Loading Structure
From Pure Premium to Gross Rate
The gross premium is constructed by dividing the pure premium by the permissible loss ratio — which implicitly applies all loadings simultaneously:
Gross Premium = Pure Premium ÷ Permissible Loss Ratio
If the pure premium is $500 and the target combined ratio is 92% (meaning the permissible loss ratio is 68%), the gross premium = $500 ÷ 0.68 = $735. The $235 margin covers acquisition costs (~15%), overhead (~10%), and profit/contingency (~7%).
Regulatory Constraint
In regulated personal lines markets (auto, homeowners), actuarially justified rates must be filed and approved by state departments of insurance before implementation — a process that can take 60–180 days and creates a lag between loss deterioration and rate adequacy recovery.
Risk Classification
Rating Variables & Risk Segmentation
A single base rate is refined through risk classification — applying relativities for characteristics that predict loss experience. In personal auto: vehicle age and type, driver age, credit score, claims history, territory, and telematics score. In commercial property: construction type, occupancy, protection class, and geographic hazard scores.
Regulatory constraints on rating variables vary significantly by state and line. Credit scoring is prohibited in some states for homeowners; gender cannot be used in personal auto in some EU markets. These constraints limit actuarial precision and create cross-subsidies between risk segments.
