# D.01.Bernegger

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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
 Author: Exam8 ID: 165927 Card Set: D.01.Bernegger Updated: 2012-08-13T23:28:05Z Folders: Description: Swiss Re Exposure Curves and the MBBEFD Distribution Clas Show Answers: