B.01.Lee

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Author:
Exam8
ID:
162744
Filename:
B.01.Lee
Updated:
2012-08-14 13:10:34
Tags:
Premium prospective retrospective trend pure rating
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Description:
The mathematics of excess of loss coverage and retrospective rating - A graphical approach
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  1. Graphical representation of E(X)
  2. Layers method to price ded & limit
  3. ILFs vs frequency
    • frequency does not matter for ILFs
  4. ILFs properties
    • I(k) is increasing at a decreasing rate
    • Miccolis consistency test: marginal P should decr as limit decr
  5. Inflation vs XS loss
  6. Excess PP ratio φ(r)
  7. 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
  8. Interpretation of Ψ(r) = φ(r) + r - 1
    • If we charge rE(X) we lose (1-r)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)
  9. Use of φ(r) and Ψ(r) for ratro rating
  10. Retro rated policies w per accident limit
    • F* ~ A* / E
    • loss elimination ratio = k = (E - A*) / E

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