Methods of calculating risk premium

Question 1

• Burning cost

Answer 1

o A burning cost approach takes the actual cost of claims during a past period of years, expressed as an annual rate per unit of exposure. This could apply to a single risk or to a portfolio of similar risks.
o The technique may be purely based on past claims without adjustment, although an improvement would be to adjust past claims for trends and develop the claims to ultimate, but often this is not practice. If trending is applied to claims, exposure should be adjusted.
o The burning cost approach is commonly applied to aggregate claims, but may also be applied to frequency and severity separately.

Question 2

• Frequency-severity (5/2)

Answer 2

o The frequency-severity approach involves analysing and projecting frequency and severity separately, fitting distributions to each, and then combining the two to calculate the risk premium.
o Advantages and disadvantages –
 The frequency-severity approach mirrors the underlying process, allows complex structures to be modelled more easily (using stochastic modelling), provides a better understanding of the data, and enables frequency and severity trends to be identified separately. It can be more accurate than the burning cost approach. However, it requires more data (by volume and detail) and it more time consuming and complex.

Question 3

• Multivariate analysis, including GLMs

Answer 3

 A large range of questions is asked at the point of sale for personal lines motor and home insurance. These questions relate to the policy, the proposer and the vehicle or house. Many of these questions do not directly measure the genuine risk factors but act as proxies instead.
 External data can be added, to help predict claims experience. It is necessary for linking fields to exist so that the external data can be attached to the internal data.

Question 4

• Original loss curves:

Answer 4

o Original loss curves are more often called:
 Property business – first loss scales, exposure curves or loss elimination functions. They show the proportion of the full value premium allocated to primary layers at different values. When showing the proportion to allocate to the excess layer rather than the primary layer, they are also called excess of loss scales.
 Causality business – increased limit factors. They give the ratio of premium for higher limits to a basic limit.
o Curves often only account for pure loss cost, but may be adapted to allow for ALAE, ULAE and a load for risk at each limit.
o The curves are closely related to the limited expected value function, which is a non-decreasing function that increases at a decreasing rate.
o Advantages and disadvantages:
 The application of exposure curves and ILFs is difficult in practice, often due to uncertainty in estimating or selecting the appropriate curves.
 However, they are relatively simple to implement, easy to explain, provide internally – consistent loss costs and can be used where there is little or no credible data.