Question

You are given: - The number of claims has a Poisson distribution. - Claim sizes have a Pareto distribution with parameters θ= 0.5 and α=6. - The number of claims and claim sizes are independent. - The observed pure premium should be within 2% of the expected pure premium 90% of the time. Determine the expected number of claims needed for full credibility.

Answer 1

To determine the expected number of claims needed for full credibility, calculate the expected pure premium by multiplying the mean claim size by the mean number of claims. The mean of a Pareto distribution with parameters θ and α is given by: μ = θ * (α / (α-1)). Substituting the values, the mean claim size is 0.6. The expected pure premium is 1.8, so the expected number of claims needed for full credibility is 1.8.

Step-by-step explanation:

To determine the expected number of claims needed for full credibility, we first need to calculate the expected pure premium. The expected pure premium is the average cost per claim, which can be found by multiplying the mean claim size by the mean number of claims. In this case, the mean claim size can be found using the parameters of the Pareto distribution: θ= 0.5 and α=6.

The mean of a Pareto distribution with parameters θ and α is given by: μ = θ * (α / (α-1)). Substituting θ=0.5 and α=6, we have: μ = 0.5 * (6 / (6-1)) = 0.5 * (6 / 5) = 0.6.

So the mean claim size is 0.6. Now, we can calculate the expected pure premium. Since the number of claims has a Poisson distribution with an average of three per week, the mean number of claims is also three. Thus, the expected pure premium is: 3 * 0.6 = 1.8.

Therefore, the expected number of claims needed for full credibility is 1.8.