
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


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)

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

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

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

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)

MBBEFD class of 2parameter exposure curves

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

Exposure curves used by non proportional prop uwrs
 can be approximated using subclass of MBBEFD
 b_{i}, g_{i} 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 Y_{14}
 c = 5 corresponds to Lloyd's curve for industrial risks

