Rate risks under alternative procedures: class plans, territories, deductibles, increased limits, coinsurance, and commercial lines mechanisms.

Two shop owners buy the same $500,000 building policy, but one sits in a flood plain and carries a $1,000 deductible while the other insures to only 60% of value. The base rate is one number; alternative procedures turn it into the price each actually pays.

A class plan sorts insureds into groups that share loss potential. You pick one group as the base class and express every other class as a relativity to it. A class with relativity 1.30 is 30% costlier than base.

Premium for a risk equals the base rate times the class relativity times exposures. You do not read relativities off raw experience blindly. You compute indicated relativities by one of three univariate methods.

The pure premium method divides each level's pure premium (losses over exposures) by the base level's pure premium. It double counts any correlation between the rating variable and other variables, because uneven exposures pull the pure premium up or down.

The loss ratio method compares each level's loss ratio to the total loss ratio, then applies that change factor to the current relativity.

Common mistakes

• Reading LER as deductible over mean loss. LER uses expected losses capped at $d$, not $300 ÷ $1,000. The cap counts every claim up to the deductible, giving 0.27 here, not 0.30.
• Using policies whose data do not observe the layer. When you move between deductibles, drop every policy whose deductible exceeds the lower deductible of the move. You may aggregate full-coverage policies and those with a deductible at or below it, because they observe the layer you need.
• Treating the coinsurance penalty as a partial-versus-total switch. The penalty depends on size, not on totality. It needs $L>0$, $F<cV$, and $L<cV$, peaks at $L=F$, and fades to zero as the loss reaches the coinsurance requirement $cV$.

Bottom line

• A class plan groups similar risks; premium equals base rate times relativity times exposures, and you compute indicated relativities by the pure premium, loss ratio, or adjusted pure premium method.
• Judge each rating variable against Finger's four categories of criteria: statistical, operational, social, and legal.
• Territories are geographic classes; pick a base unit, isolate the geographic signal, then smooth by distance or adjacency and cluster the results.
• A deductible credit equals the LER; the censored variant prices a move between deductibles using only policies with a deductible at or below the lower deductible, the ones that observe the layer.

Exam shortcut

For any deductible problem, compute LER as expected losses capped at $d$ over the ground-up mean, then multiply the base loss cost by $(1 - \text{LER})$. To move between deductibles, use the censored LER over losses above the current deductible, and drop any policy whose deductible is above the lower deductible of the move, because it does not observe the whole layer.

The full lesson (about 5,680 words, 38 min read) adds 12 worked examples, all 9 common mistakes, a self-check, free in the app.

Learning objectives

• A14

Browse all free Exam 5 lessons or jump into free Exam 5 practice questions.