[[Actuarial Notes Wiki|Wiki]] / [[Exam 5 (CAS)]] / **Pure Premium Analysis** ## Definition ==Pure Premium Analysis== is the examination of expected losses per exposure unit, calculated as total losses divided by exposures, used to assess pricing adequacy and identify trends. ## Formula ``` Pure Premium = Total Losses / Total Exposures Or equivalently: Pure Premium = Frequency × Severity ``` ## Uses ### Diagnostic Tool ``` Track pure premiums by: - Accident year - Territory - Class - Coverage Identify: - Pricing adequacy - Emerging trends - Mix changes ``` ### Comparison to Rates ``` Rate Adequacy Ratio = Pure Premium / (Rate × Permissible Loss Ratio) Example: Pure Premium: $250 Current Rate: $350 Target Loss Ratio: 65% Expected Pure Premium: $350 × 0.65 = $227.50 Ratio: $250 / $227.50 = 1.10 (10% inadequate) ``` ## Example ``` Territory Analysis: Territory Exposures Losses Pure Premium Urban 5,000 $1,500,000 $300 Suburban 8,000 $1,760,000 $220 Rural 3,000 $450,000 $150 Urban is twice as costly as Rural Relativities: Urban 2.00, Suburban 1.47, Rural 1.00 ``` ## Related Concepts - [[Pure Premium Method#Definition]] - [[Frequency Analysis#Definition]] - [[Severity Analysis#Definition]] ## References - Werner & Modlin, Chapter 5