17.7 Exercises

17.1 An insurance company has decided to establish its full-credibility requirements for an individual state rate filing. The full-credibility standard is to be set so that the observed total amount of claims underlying the rate filing would be within 5% of the true value with probability 0.95. The claim frequency follows a Poisson distribution and the severity distribution has pdf

equation

Determine the expected number of claims necessary to obtain full credibility using the normal approximation.

17.2 For a particular policyholder, the past total claims experience is given by X1,…, Xn, where the Xjs are i.i.d. compound random variables with Poisson parameter λ and gamma claim size distribution with pdf

equation

You also know the following:

1. The credibility factor based on number of claims is 0.9.
2. The expected claim size αβ = 100.
3. The credibility factor based on total claims is 0.8.

Determine α and β.

17.3 For a particular policyholder, the manual premium is 600 per year. The past claims experience is given in Table 17.1. Assess whether full or partial credibility is appropriate and determine the net premium for next year’s claims assuming the normal approximation. Use r = 0.05 and p = 0.9.

Table 17.1 Data for Exercise 17.3.

17.4 Redo Example 17.2 assuming that Xj is ...

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