QA Bank Part 4

Question 1

12 Factors affecting the number of rating factors selected when modelling experience for pricing purposes

Answer 1

• the exact purpose of the exercise
• the number of rating factors currently being used in the rating
• the number of rating factors used for pricing by competitors
• the capacity of the model being used
• the time available to perform the investigation
• IT (or other) restrictions on how many rating factors can be incorporated into rating algorithms
• the quantity of data available
• the level of detail of the data available
• the judgement applied by the modeller
• sales channel (may affect the level of complexity required)
• level of competition in the market for the class of business being modelled
• adjustments made to data either in cleaning trending or developing.

Question 2

Define experience rating

Answer 2

A system whereby the premium of each individual risk depends, at least in part, on the actual claims experience of that individual risk.

Question 3

4 Arguments supporting the use of experience rating in general insurance

Answer 3

• premiums better reflect the risk
• encourages better behaviour by policyholders
• discourages small claims and associated admin costs
• might be wanted by policyholders

Question 4

4 Main problems that can arise when attempting to derive increase limit factors (ILFs) for casualty (liability) business.

Answer 4

Lack of volume and of credibility of data

Information about large losses may be lost, due to the impact of policy limits

Adjusting for trend:

• – working out what the adjustment should be
• – adjusting the ILFs appropriately (as the impact of trend may vary by size of loss)

Many claims will still be open:

• – these may take a long time to settle
• the final claim amount may be very different from the current case estimate.

Question 5

Describe the various systems used in experience rating

Answer 5

PROSPECTIVE RATING
Premium at renewal depends on the experience prior to the current renewal date.

RETROSPECTIVE RATING
An initial premium is adjusted at the end of the period of cover to reflect claims experience in the year of cover.

The system can be based either on the number of claims or amounts.

For amounts-based systems, a credibility rating is used.
The credibility of claims experience is the measure of the weight to be attached to the experience of the particular risk compared with the experience of the insurer’s portfolio of similar risks.

Question 6

Describe the process of Multivariate analysis to establish principal rating factors

Answer 6

PAST CLAIMS AND EXPOSURE DATA is required.
Prepare details of claim numbers and exposure for all combinations of rating factors.

Given the lack of data, grouping levels of rating factors may be necessary.
Spacial smoothing or vehicle classification methods could be used for grouping levels of factors such as postcode and make/model of motorcycle.

ONE-WAY TABLES of each rating factor in isolation can be used to check the reasonableness of the prepared data and will give a preliminary indication of the effect of each factor in terms of claim frequency.

TWO-WAY TABLES can be used to help understand CORRELATIONS between pairs of rating factors and to indicate which factors may be affected by the removal or inclusion of any other factor in the multivariate analysis.

May need to adjust for:

• changes in policy conditions
• mid-year endorsements (allocate proportion to each cell)
• unreported claims, especially latest year’s data.

Investigate frequency for each major claim type separately (e.g. fire, theft, damage, liability, …).

Look for TRENDS OVER TIME and try to explain them

Use a STATISTICAL RATING MODEL (eg a GLM) to produce expected claim frequencies for all combinations of rating cells chosen.

Test a range of models to see which gives the best fit to the actual data values. By comparing actual versus expected claim frequencies for different models, we can assess the error terms.

We can then decide which model gives the best fit to the data.

Question 7

4 Common assumptions made when carrying out a multivariate analysis

Answer 7

• Choice of the model: multivariate, GLM, generalised non-linear model, generalised additive model.
• The link function
• Grouping within rating factors
• Type of error structure

GLMs are commonly used as they are not too complex to run, but are based on a sound statistical framework.

A common choice for claim frequency error structure is a Poisson assumption.

This is because it provides a good fit to claim frequency data and ensures that model frequencies stay positive.