A monoline company writes $60 million in premium and begins the year with
a surplus of $60 million. determine the capital at risk at the 99% level
after 2 years, given the following information:
Annual Aggregate Loss Distribution
Size of Annual Aggregate Loss: Probability:
90% of written premium 90%
150% of written premium 10%
-Premium writings in a year are equal to the level of surplus at the
beginning of that year.
-Earned premiums in a given year equal written premiums in that year.
-Expenses=taxes=investment income=zero.
-Profits or losses flow directly into or out of surplus.
-Loss distribution remains constant.
I understand how to calculate the possible surpluses and their
probabilities. The solution offered on the CAS exam solutions calculates
the premium at risk to be $60 mill - $33 mill = $27 mill
I do not understand this logic. Please help. Thanks.