Your company decided a few years ago to enter the lucrative business of selling alien abduction policies. This business has performed extremely well in the past, with an observed loss ratio consistently at 0% over the last five years.

Building on this good fortune, the underwriting manager has decided to design a new policy that covers post-traumatic stress disorder (PTSD) arising from UFO sightings.

The pricing factors of the policy (which is sold to individuals) are the following:

• Distance of habitation from renowned sighting areas (≤100 km, between 100 km and 500 km, above 500 km)

• Marriage status (married/not married)

• Number of previous sightings by the policyholder (0, 1, more than 1)

• Occupation of policyholder (pilot, other)

The compensation is a flat FRD 10,000 (FRD = Freedonian dollars) for each episode (unlimited number of episodes per year).

i. Find a suitable generalised linear model for the expected losses to the policy, which includes all the factors above. Assume that all factors are non-interacting.

ii. Describe the process by which you could calibrate this model if you had sufficient data.

iii. Repeat the exercise

(a) by assuming that the number of previous sightings and the occupation are interacting.

You soon find out that based on the relatively meagre loss data experience at your disposal, you will not be able to fully calibrate model (i), and you decide to use a simplified version of the model found in (i), i.e. a sub-model of (i) with fewer pricing factors.

iv. Explain what strategy you would use to determine which sub-model of (i) is the most adequate to describe the risk of a policyholder.