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IAI Nov 2012

V

Visakha

Member
The aggregate claim process from a portfolio of 1000 one year health insurance policies, each with monthly premium of Rs. 200 (payable in advance), is a compound Poison process. The expected number of claims per month is 1. The policy covers three types of health risk events viz. Minor, moderate and major, for which the claim amounts are Rs. 100000, Rs. 250000 and Rs 500000 respectively. The probabilities that a claim is for a Minor, Moderate and Major risk event are 70%, 25% and 5%, respectively. Claims are settled at the end of each month. The insurer holds initial surplus of Rs. 90000.
Calculate the probability of ruin at the end of the first month.

If I solve the question by finding the mean and variance of S(1) and then solving as P[S(1) > 290000] = P[N(0,1) > .707] I get the answer as .23978

However the question has been solved differently in the solution via the
Case I: N(1)= 0.
Case II: N(1)=1,X(1) =/= 500,000.
Case III: N(1) = 2, X(1) = X(2) = 100000
And they get the answer as .1925

How do we know which way to use when?
 
You should only use a normal approximation if the question tells you to calculate the probability approximately or if an exact calculation is very time consuming.

Here it's easy to calculate the exact probability, and that's what you're expected to do. :)
 
Julie, considering that the original question is for 8 marks, how many marks could be deducted if we follow the Normal approximation method?
 
It's hard to know without seeing the markscheme. But for the IFoA you would lose between half of the marks to all of them.
 
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