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?
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?