What are the determinants of demand.

The generalised linear model (GLM) may be expressed as: XUB, + + 8 (i) Express the above in matrix form, and give a definition for each term. [4] A pricing actuary has fitted a GLM with a binomial error structure to model the probability that customers renew their policy at the end of the policy year. The fitted model has two factors: premium change at renewal and geographical area. Each of these factors has three levels, as shown below, along with the linear predictor estimates for each level. Premium change at renewal Linear predictor estimates +5% 2.0336 Geographical area Linear predictor estimates 0.0000 0.9734 1.4483 The linear predictor for the base level is 1.9465. (ii) Explain the concept of the base level in the context of the GLM described above. [1] (iii) Determine the probability of renewal for a policyholder in geographical area B whose premium change at renewal is -7%. [3] (iv) Suggest ways in which a customer retention model could be used by the insurance company. [4]7 The numbers and amounts of claims have been collected by a general insurance company for the last four years. It is believed that the number of claims incurred follows a Poisson distribution, and the severity of claims follows a gamma distribution. Explain how Monte Carlo simulation could be used to model the aggregate claim amount distribution. [10] 8 (i) Describe the cover provided by employers' liability insurance. (2] A general insurance company provides employers' liability insurance to a paint manufacturer. The pricing actuary intends to use a frequency-severity approach to rate the product. (ii) Suggest, with reasons, adjustments to the claim data that might be appropriate in order to perform this exercise. [5] The broker placing the business has informed the insurance company that the paint manufacturer wishes to reduce the premium by paying an excess on each claim. The paint manufacturer has suggested an excess of (5,000, but the broker would like to know how the premium would change if the excess was (10,000. (iii) Explain how the pricing actuary should determine the difference in premium between these two excess levels. [3]