Chapter 19 - Methods of Calculating Risk Premium

Question 1

Allocated loss adjustment expenses (ALAE)

Answer 1

The expenses incurred in handling and settling claims. These can be directly attributed, and hence allocated, to a line of business.

Question 2

Burning cost

Answer 2

The actual cost of claims paid or incurred during a past period of years expressed as an annual rate per unit of exposure. The claims should be adjusted for inflation and any outstanding claims

Question 3

Deep pocket syndrome

Answer 3

A situation where claims are made based on the ability of the defendant to pay rather than on share of blame. An injured party will try to blame the party with the greatest wealth (i.e. the one with the deepest pocket) where there is more than one potential defendant

Question 4

Exposure rating

Answer 4

A method of calculating the premium that is based on external data or benchmarks. The premium of each individual insured does not depend on the actual claims experience of the insured. Instead, the amount of exposure that the insured brings to the insurer and the experience for comparable risks is used to calculate the premium rate

Question 5

From the ground up

Answer 5

A statement of the original insurer’s experience of a class of business offered for reinsurance is said to be from the ground up when it shows the number and distribution by amount of all claims however small, even though reinsurance is required for large claims only

Question 6

Generalised linear model (GLM)

Answer 6

A flexible generalisation of ordinary least squares regression. The GLM generalises linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value

Question 7

Increased limit factors

Answer 7

Factors which estimate the cost for a new limit as a multiple of the basic (original) limit

Question 8

Per-claim basis

Answer 8

The original loss curves are based on the amounts that will be paid to each individual claimant for losses that arise from one incident

Question 9

Per-occurrence basis

Answer 9

The original loss curves are based on the total amounts paid to all plaintiffs that arise from one incident

Question 10

Points rating system

Answer 10

A system for calculating the office premium by relating it to points associated with each cell within a rating factor. The higher the risk associated with the cell, the higher the points and the higher the premium

Question 11

Aggregate deductible

Answer 11

The maximum amount that the insured can retain within their deductible when all losses are aggregated

Question 12

Non-ranking deductibles

Answer 12

The non-ranking component of a deductible (applied to each individual loss) does not contribute to an insured’s aggregate deductible. Stops being applied after aggregate deductible limit has been reached

Question 13

Deductible

Answer 13

The amount which, in accordance with the terms of the policy, is deducted from the claim amount that would otherwise have been payable and will therefore be borne by the policyholder

Question 14

Ranking deductible

Answer 14

The ranking component of a deductible does contribute to an insured’s aggregate deductible. The deductible here is applied sequentially for claims coming in until the aggregate deductible amount is reached. This is assessed before the non-ranking deductible.

Question 15

Trailing deductible

Answer 15

The amount that is retained by the insured for each individual loss once the aggregate deductible has been fully eroded

Question 16

Per occurrence limit

Answer 16

The maximum amount that the insurer can retain for each individual loss

Question 17

Annual aggregate limit

Answer 17

The maximum amount that the insurer can retain when all losses for an annual policy period are aggregated

Question 18

Loss sensitive / Swing rated premiums

Answer 18

A form of experience rating. Therese are premiums that depend, at least in part, on the actual claims experience of that risk in the period covered. They will usually be applied in the form of a deposit and adjustment premium

Question 19

Chi-square goodness of fit test

Answer 19

Statistical test used to asses the correctness of fit of a distribution. Done by testing the expected vs. actual number of observations in chosen buckets across a distribution. SIG( [Oi - Ei]^2 / Ei) where i is one of n buckets. Ei are the expected number of observations for bucket i given the distribution and Oi are the actual number of observations in bucket i

Question 20

Kolmogorov-Smirnov (K-S) statistic

Answer 20

Statistical test used to asses the correctness of fit of a distribution. Done by assessing the largest difference between the empirical distribution function (from data) and the cumulative distribution function from the theoretical function. This distance is compared to a critical value from the K-S tables

Question 21

Anderson-Darling statistic

Answer 21

Statistical test used to asses the correctness of fit of a distribution. It is a distance test to see how likely it is that the empirical values come from a distribution. Based off the following formula:
AD = -n - (1/n)SIG( (2i-1){ln(F(Xi) + ln(1- F(X_n-i+1)}.
n: sample size
i: the ith data point in the sample
F: The theoretical distribution being fit
This is compared to a critical value and the null hypothesis (that the data does come from the theoretical distribution) is rejected if it less

Question 22

Multivariate model

Answer 22

A model which allows for the effects of various different combinations of variables to be estimated for a given dependent/explained variable

Question 23

Propensity

Answer 23

The tendency towards a particular way of behaving

Question 24

Relativities

Answer 24

Numbers that quantify the level of risk in one category compared to that in another

Question 25

Classification

Answer 25

The grouping of levels of factors