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Old 05-09-2018, 05:21 PM
loco_pabs loco_pabs is offline
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Each life within a group medical expense policy has loss amounts which follow a compound Poisson process with . Given a loss, the probability that it is for Disease 1 is 1/16.

Loss amount distributions have the following parameters:
Code:
                              Mean per loss             Std. Dev. per loss
--------------------------------------------------------------------------
Disease 1                         5                              50
Other Diseases                   10                              20
Premiums for a group of 100 independent lives are set at a level such that the probability (using normal approximation to the distribution for aggregate losses) that aggregate losses for the group will exceed aggregate premiums for the group is 0.24.

A vaccine which will eliminate Disease 1 and costs 0.15 per person has been discovered.

Define:
A = the aggregate premium assuming that no one obtains the vaccine, and
B = the aggregate premium assuming that everyone obtains the vaccine and the cost of the vaccine is a covered loss.

Calculate A/B.
-----------------------------------------------------------------------------------------

Why are we able to multiply 0.16 () by each of the probabilities for Disease 1 or Other diseases?
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Old 05-22-2018, 09:27 PM
Academic Actuary Academic Actuary is online now
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Quote:
Originally Posted by loco_pabs View Post
Each life within a group medical expense policy has loss amounts which follow a compound Poisson process with . Given a loss, the probability that it is for Disease 1 is 1/16.

Loss amount distributions have the following parameters:
Code:
                              Mean per loss             Std. Dev. per loss
--------------------------------------------------------------------------
Disease 1                         5                              50
Other Diseases                   10                              20
Premiums for a group of 100 independent lives are set at a level such that the probability (using normal approximation to the distribution for aggregate losses) that aggregate losses for the group will exceed aggregate premiums for the group is 0.24.

A vaccine which will eliminate Disease 1 and costs 0.15 per person has been discovered.

Define:
A = the aggregate premium assuming that no one obtains the vaccine, and
B = the aggregate premium assuming that everyone obtains the vaccine and the cost of the vaccine is a covered loss.

Calculate A/B.
-----------------------------------------------------------------------------------------

Why are we able to multiply 0.16 () by each of the probabilities for Disease 1 or Other diseases?
The Poisson has the property that if the outcomes fall into different classes with known probabilities, then the number in each class will have its own Poisson distribution.
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Old 05-22-2018, 11:58 PM
ARodOmaha ARodOmaha is offline
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Quote:
Originally Posted by Academic Actuary View Post
The Poisson has the property that if the outcomes fall into different classes with known probabilities, then the number in each class will have its own Poisson distribution.
Yes, that is why the problem states that it is a "compound Poisson", i.e. it can be separated into proportional Poisson's. Conversely, you can add Poisson's together. (I learned this after getting that exact problem wrong.)
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