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:
loss amount probability
0 0.4
1 0.3
2 0.2
3 0.1
iii. the stop-loss insurance has a deductible of 1 for the group.

calculate the net stop-loss premium.
a. 2.00
b. 2.03
c. 2.06
d. 2.09

Answer 1

To answer the user's question, the net stop-loss premium calculated based on the given probabilities and deductible for a three-person group is $2.06.

Step-by-step explanation:

The calculation of a net stop-loss premium involves determining the expected payment by the insurance company for losses exceeding the deductible. In this case, with a deductible of 1 for the three-person group and given the independent loss amounts with the specified probabilities, the expected loss amount for a person can be derived by multiplying each loss amount by its corresponding probability. Subsequently, the total expected loss for the entire group is aggregated, after which the deductible is applied to compute the net stop-loss premium.

To find the net stop-loss premium, each loss scenario for an individual is considered, including the loss deductibles for the entire group. Given the loss distribution, the calculations yield the expected loss beyond the deductible. Finally, the sum of these expected losses gives the net stop-loss premium, which in this particular case is $2.06.