D.01.Bernegger

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Author:
Exam8
ID:
165927
Filename:
D.01.Bernegger
Updated:
2012-08-13 19:28:05
Tags:
exposure rating first loss scale curve swiss re
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Description:
Swiss Re Exposure Curves and the MBBEFD Distribution Clas
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  1. Exposure rating
    • similar size risks from same risk category placed in bands
    • risks in a band assumed to be homogeneous
    • can use a single loss dist to model
    • fit 1 exposure curve per band
  2. Exposure curve formula
  3. First loss scales / exposure curves
    • gives proportion of P allocated to limited primary layers
    • % value of imposing a deductible
    • limits usually expressed as % of sum insured (SI), maximum probable loss (MPL) or estimated maximum loss (EML)
  4. Notes on exposure curve table
    • can allow % > 100% of building value (other covg)
    • implicit assumption that same exposure curve applies regardless of the size of the insured value
  5. Analytical exposure curve
    • used when looking for values btwn 2 discrete curves
    • (-) must fill certain conditions which restrict the range of param
    • (-) practical issues w fctns w >2 param
  6. Deriving distribution function from exposure curve
    • G(d) is increasing concave on [0,1]
    • G'(d) = [1 - F(d)] / E(X)
    • F(x) = 1 - G'(x) / G'(0)   (1 if x = 1)
    • μ = E(x) = 1 / G'(0)
    • p = 1 - F'(1-) = G'(1) / G'(0)
    • G'(0) ≥ 1 ≥ G'(1) ≥ 0
    • 0 ≤ p ≤ μ ≤ 1
  7. Unlimited distribution
    • normalize deductible to some other ref loss like sum insd
    • G(d) still concave increasing on [0,1]
    • M = E(x) = 1 / G'(0)
    • G(∞) = 0 (no total loss)
  8. MBBEFD class of 2-parameter exposure curves
  9. Curve fitting
    • there exists exactly 1 dist fctn belonging to MBBEFD class for each given pair of functional p and μ
    • if first 2 moments are known we can find g and b
  10. Exposure curves used by non proportional prop uwrs
    • can be approximated using subclass of MBBEFD
    • bi, gi evaluated for each curve i
    • curve modeled as a fctn of single parameter c
    • c{1.5,2.0,3.0,4.0} corresponds to Swiss Re curve Y1-4
    • c = 5 corresponds to Lloyd's curve for industrial risks

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