The question mentions that claim can only arise on 1st Aug each year and the policy has commenced by 1st Jan 2001. In sub question (ii) (a), the question states that probability of ruin (U,t1)= pr. of ruin (U,t2) where 7/12<t1 and t2<19/12. This does not make any sense to me because, by month 19 in the 2nd year, one instance of the date, 1st August would have elapsed and some claims could have arisen. Hence, there is no reason why the probability of ruin would be same (i.e. nil as claimed in the answer) for both the time period. answer to (ii) b is also calculated with period 7/12 instead of 1. Unable to understand how 7/12 is made equivalent to 1 year as well. Please help.
I think what is written there doesn't mean that the prob. of ruin is NiLL. See, there are two time periods. First is of greater than 7 months (t1>1Jan to 31 july). So, we assume that it will include 1st August. And the claim can occur in this time period once. Second time period is less than 19 months(t2< 1Jan,first year to 31 july of second year). Since it's less than 19 months, it will not include 1st August of second year. Claim can occur in this time period only once as before. So, the prob. of ruin for both time periods is same.
What they have written here is that: For a year after 1st August of first year ( 2 august of frst year to 31 july of second year) , there are no claims and the insurer is receiving premium income. In this particular time period i.e. from 2nd August of first year till t2, there are no claims. But it doesn't mean that the prob. of ruin at time t1 and t2 is NILL, but this prob. is same for both time periods.
