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AAdmin
Jun 02'22

Exercise

A portfolio of annual policies are classified into two classes: class A and class B. You are given the following assumptions about the policies:

  • Claim size is always 100 for class A policies and 200 for class B policies
  • The probability of observing more than one claim per policy is zero for all policies in the portfolio
  • The probability of observing a single claim in a year is 0.05 for class A policies and 0.03 for class B policies
  • 25% of the policies in the portfolio belong to class A
  • The expected loss for class A policies is 0.9 times the premium and the expected loss for class B policies is 0.8 times the premium.

Using the normal approximation, determine the smallest number of policies required in the portfolio that is divisible by 4 and large enough that the portfolio is profitable at least 95% of the time.

  1. 1,020
  2. 1,032
  3. 1,672
  4. 1,680
  5. 1,688
AAdmin
Jun 02'22

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