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Graphical representation of E(X)

Layers method to price ded & limit

ILFs vs frequency
 frequency does not matter for ILFs




Properties of φ(r) and Ψ(r)
 φ'(r) = G(r) and φ''(r) = f(r)
 charge is decreasing at a decreasing rate
 Ψ'(r) = F(r) and Ψ''(r) = f(r)
 savings increase at an increasing rate

Interpretation of Ψ(r) = φ(r) + r  1
 If we charge rE(X) we lose (1r)E(X)
 (1) φ(r) = insured loss above r
 (2) Ψ(r) = savings from losses below r
 For a correctly priced policy, r = 1 and φ(r) = Ψ(r)

Use of φ(r) and Ψ(r) for ratro rating

Retro rated policies w per accident limit
 F* ~ A* / E
 loss elimination ratio = k = (E  A*) / E

