Bernegger Flashcards
Exposure curve G(d)
E[X; dIV] / E[X]
Four conditions for a valid normalized exposure curve
G(0) = 0
G(1) = 1
G’(d) >= 0
G’‘(d) <= 0
G’(d) formula
(1 - F(d)) / E[y]
Expected value using exposure curve
µ = 1 / G’(0)
µ = expected severity / MPL
Probability of total loss, exposure curve
p = G’(1) / G’(0)
Conditions for MBBEFD parameters
g >= 1
b >= 0
Problems with exposure rating, Bernegger
How to divide total premiums to each risk size group between cedant and reinsurer
Solved in two steps:
- Estimate expected loss by applying ELR to gross premiums
- Divide expected losses into retained and ceded portions with help of loss distribution functions
Curve fitting, if p and µ are given
g = 1/p
b can be determined based on µ; iterative process
MBBEFD curve fitting if µ and σ are given
- p* = E[y2] = µ2 + σ2
- g* = 1/p* and b* can be based on µ
- Recalculate p*
- Repeat until E*[y2] is close enough to E[y2]
Swiss Re curves
c = {1.5, 2.0, 3.0, 4.0} go very well with Swiss Re curves {Y1, Y2, Y3, Y4}
c = 5.0 coincides with Lloyd’s curve for industrial risks