B.1. Distributions for Actuaries

Question 1

Panjer’s recursive algorithm formula

Answer 1

Question 2

Graph of expected loss with limit and retention

Answer 2

Question 3

Excess severity formula with retention and limit

Answer 3

Question 4

CDF formula for excess losses

Answer 4

Question 5

Graph of common excess severity distributions

Answer 5

Question 6

Coefficient of variation for excess layers formulas

Answer 6

Question 7

Pdf, mean and variance for excess claim counts

Answer 7

Question 8

Impact of inflation on excess layer severity

Answer 8

Question 9

Impact of severity inflation on excess counts

Answer 9

Question 10

Impact of severity inflation on aggregate layer losses

Question 11

Mean and variance of aggregate layer losses

Answer 11

Question 12

Two things covered by a risk charge

Answer 12

1. Random deviations of losses from expected values (process risk)
2. Uncertainty in the selection of the parameters describing the loss process (parameter risk)

Question 13

ILF and premium for layer formulas

Answer 13

Question 14

First and second derivative of ILF for consistency test

Answer 14

Question 15

Risk loaded ILF formula

Answer 15

Question 16

2 options for calculating risk load

Answer 16

Question 17

Risk load for a layer

Answer 17

Question 18

ILF with a per-claim limit and aggregate limit

Answer 18

Question 19

Pure premium and loss elimination ratio with straight deductible and basic limit

Answer 19

Question 20

Premium with straight deductible and increased limit

Answer 20

Question 21

Pure premium and loss elimination ratio with franchise deductible and basic
limit

Answer 21

Question 22

Pure premium after inflation above straight deductible with limit

Answer 22

Question 23

Impact of trend net of straight deductible with limit

Answer 23