Consider a car owner who has an 80% chance of no accidents in a year. For simplicity, assume that there is a 10% probability that after the accident the car will need repairs costing $500, an 8% probability that the repairs will cost $5,000, and a 2% probability that the car will need to be replaced, which will cost
$15,000. Based on this information, the probability distribution, f(x), of the random variable, X, loss due to accident, is:
f(x) =
0.8 x = $0
0.10 x = $500
0.08 x = $5,000
0.02 x = $15,000
where the first column is the probability of the event (i.e. P(x=0) =0.8) and the second is the severity.
Assuming risk retention, calculate the object risk to the car owner. Show ALL your work.
Now consider an insurance company that will reimburse repair costs resulting from accidents for 100 car owners, each with the same probabilities and losses as in part a). Calculate the objective risk for the insurance company. How is this number compared to that of part a)? Explain. Show ALL your work.
Suppose that the insurance company provides insurance to the same 100 car owners but now it introduces a deductible of $500. The claim payment distribution for EACH policy would now be:
f(y)=
0.90 x = $0 or $500 y = $0
0.08 x = $5,000 y = $4,500
0.02 x = $15,000 y = $14,500
where
Consider a car owner who has an 80% chance of no accidents in a year. For simplicity, assume that there is a 10% probability that after the accident the car will need repairs costing $500, an 8% probability that the repairs will cost $5,000, and a 2% probability that the car will need to be replaced, which will cost
$15,000. Based on this information, the probability distribution, f(x), of the random variable, X, loss due to accident, is:
|
f(x) = |
|
0.8 x = $0 |
|
0.10 x = $500 |
|
0.08 x = $5,000 |
|
0.02 x = $15,000 |
where the first column is the probability of the event (i.e. P(x=0) =0.8) and the second is the severity.
Assuming risk retention, calculate the object risk to the car owner. Show ALL your work.
Now consider an insurance company that will reimburse repair costs resulting from accidents for 100 car owners, each with the same probabilities and losses as in part a). Calculate the objective risk for the insurance company. How is this number compared to that of part a)? Explain. Show ALL your work.
Suppose that the insurance company provides insurance to the same 100 car owners but now it introduces a deductible of $500. The claim payment distribution for EACH policy would now be:
|
f(y)= |
|
0.90 x = $0 or $500 y = $0 |
|
0.08 x = $5,000 y = $4,500 |
|
0.02 x = $15,000 y = $14,500 |
where
