Question

For a stop-loss insurance on a three-person group:

i. Loss amounts are independent:
ii. The distribution of loss amount for each person is:
iii: The stop-loss insurance has a deductible of 1 for the group

Loss Amount Probability
0 0.4
1 0.3
2 0.2
3 0.1

Calculate the net stop-loss premium:
2.00
2.03
2.06
2.09
2.12

Answer 1

To calculate the net stop-loss premium, you use the provided probability distribution to find the expected value of claims exceeding the deductible, which reflects a fair premium that covers claims, costs, and profits.

Step-by-step explanation:

The student asked to calculate the net stop-loss premium for a three-person group with independent loss amounts and a given probability distribution for each person. A deductible of 1 for the group implies that losses only start to be covered once the group as a whole exceeds this amount. The distribution of loss amounts has probabilities of 0.4, 0.3, 0.2, and 0.1 for amounts 0, 1, 2, and 3 respectively. To find the net stop-loss premium, we need to consider the expected value of a claim exceeding the deductible.

When it comes to insurance, actuarial fairness means setting a premium so that the average payments into the insurance cover the average claims, company costs, and allow for profits. The premiums must reflect the risk group to which a person belongs. The loss distribution table provided is the basis for calculating the expected loss, and thereby, the premium that ensures actuarial fairness.