Bahnemann

Question 1

Panjer’s Recursive Algorithm

Answer 1

Question 2

Size view of losses

Answer 2

Question 3

Layer view of losses

Answer 3

Question 4

Expected losses in a layer

Answer 4

E[X; a; l] = E[X; a + l] - E[X; a]

Question 5

Excess loss conditional on a claim exceeding retention

Answer 5

Mean residual life at a

Question 6

Graphs of excess severity

Answer 6

Question 7

Mean and variance of excess claim counts

Answer 7

p = probability that a loss exceeds a

Question 8

Impact of inflation in fixed excess layer

Answer 8

Question 9

Impact of severity inflation on excess counts

Answer 9

Question 10

Impact of severity inflation on aggregate losses

Answer 10

Question 11

Mean and variance of aggregate losses in a layer

Answer 11

Claim contagion parameter (accounts for claims not being independent of each other)

Question 12

What the risk charge covers

Answer 12

Contingencies such as process and parameter risk

Question 13

ILF assumptions

Answer 13

1. All UW expenses and profit are variable and do not vary by limit
2. Frequency and severity are independent
3. Frequency is the same for all limits (may not be true due to adverse/favorable selections)

Question 14

Price of a layer of coverage using ILFs

Answer 14

Question 15

Consistency in ILFs

Answer 15

Increasing and doing so at a decreasing rate.

Premium for successive layers of coverage of constant width will be decreasing

Violation: adverse selection, lawsuits influencing size of limits (frequency would not be the same)

Question 16

Risk loaded ILFs

Answer 16

Question 17

Risk load: Miccolis approach

Answer 17

Question 18

Risk load: ISO approach

Answer 18

Question 19

Premium for policy with limit l and deductible d

Answer 19

Question 20

Pure premium after inflation

Answer 20

Question 21

LER relationship for the three different deductible types

Answer 21

Straight

Diminishing

Franchise

Question 22

Franchise deductible

Answer 22

Loss is truncated but not shifted

Question 23

Diminishing deductible

Answer 23

Question 24

Advantage/disadvantage of Panjer’s

Answer 24

Good for small frequency of claims

Only a single severity distribution can be used

Question 25

Issues with using lognormal distribution

Answer 25

No ability for loss-free scenario (ln 0 is undefined) No easy way to reflect impact of changing per occurrence limits on aggregate limit

Question 26

Theoretical curve fit for excess severity if curve is flat

Answer 26

Exponential

Question 27

Theoretical curve fit for excess severity if curve is linear

Answer 27

Pareto

Question 28

Theoretical curve fit for excess severity if curve is decreasing exponentially

Answer 28

Gamma

Question 29

Theoretical curve fit for excess severity if curve curves up

Answer 29

Lognormal

Question 30

Theoretical curve fit for excess severity if curve is concave down

Answer 30

Weibull

Question 31

Issue with fitting excess severity curves

Answer 31

Data usually thin and volatile at the higher amounts -- difficult to see a pattern

Question 32

Pricing a layer of coverage and applying a risk load

Answer 32

Can't simply subtract risk loaded ILFs (incorrect resulting risk load)

Question 33

ILFs that account for both claim and aggregate limits

Answer 33

E[S_l;L] / (E[N] x E[X;b])

Question 34

Impact of inflation on deductibles

Answer 34

Question 35

ILF after inflation

Answer 35

ILF of the deflated limit DIVIDED by the ILF of the deflated basic limit

Question 36

Basic pure premium after inflation

Answer 36

Freq x Sev x (1 + t) x deflated basic limit