Bernegger

Question 1

Exposure curve G(d)

Answer 1

E[X; dIV] / E[X]

Question 2

Four conditions for a valid normalized exposure curve

Answer 2

G(0) = 0

G(1) = 1

G’(d) >= 0

G’‘(d) <= 0

Question 3

G’(d) formula

Answer 3

(1 - F(d)) / E[y]

Question 4

Expected value using exposure curve

Answer 4

µ = 1 / G’(0)

µ = expected severity / MPL

Question 5

Probability of total loss, exposure curve

Answer 5

p = G’(1) / G’(0)

Question 6

Conditions for MBBEFD parameters

Answer 6

g >= 1

b >= 0

Question 7

Problems with exposure rating, Bernegger

Answer 7

How to divide total premiums to each risk size group between cedant and reinsurer

Solved in two steps:

1. Estimate expected loss by applying ELR to gross premiums
2. Divide expected losses into retained and ceded portions with help of loss distribution functions

Question 8

Curve fitting, if p and µ are given

Answer 8

g = 1/p

b can be determined based on µ; iterative process

Question 9

MBBEFD curve fitting if µ and σ are given

Answer 9

1. p* = E[y²] = µ² + σ²
2. g* = 1/p* and b* can be based on µ
3. Recalculate p*
4. Repeat until E*[y²] is close enough to E[y²]

Question 10

Swiss Re curves

Answer 10

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