Q. 10) An insurer covers a portfolio of risks where claims arrive as a Poisson process at the rate of one per year, and the claim size is Rs. 1000 (fixed). The insurer has an initial asset of Rs. 400 and receives premium at the rate of Rs. 1200 per year. Determine the probabilities of ruin within the first year. Can anyone please explain me the answer?
This really is quite straight forward simple case. Given that you have total income of 1600 after one year and each claim is a fixed 1000 I'm sure you can quickly work out how many claims will ruin the insurer...
I am unable to understand the solution given indicative solution. the given solution is provided below-: P(ruin within first year) P(ruin in first year) = 1 – P(no ruin in first year) = 1 – P(no ruin | 0 claim in first year) x P(0 claim) – P(no ruin | 1 claim in first year) x P(1 claim) = 1 – 1.e-1 – P(Claim after 8/12 year) e-1 = 1 – e-1 (1 + e-2/3). the coloured line is my problem. Why have they used 8/12th of the year... the question does not specify when exactly claim arise. Thank you for your reply.
Thank you for your reply. But I still don't get it why 8/12. The question does not specify that claims arise in the 8th month of the year. can i write 6/12 or 5/12 or any other number?(provided that its within a year). Thank you for your patience.
Sorry didn't look at your follow-up post in light of the original question. There is clearly a mistake here.
