I do not have a solution to this question and it really bugs me that I cannot derive the formula. Could anybody help me and explain? I know that the time of first claim follows and exponential distribution and that the probability of ruin simply occurs when U + (1+theta)*E(X)*E(N) - S(t)<0 but I have trouble deriving the probability that ruin occurs at first claim, which is 1 - exp[ (-1/1+theta) * (1 - U/d) ] we are given: U, theta, claim to be a fixed amount of d, N follows Poisson.
This question was repeated in September 2005 Q1 but with a loading factor of 0.2. However the issue is you forgot to do the premium income per unit time multiplied by the time in your U(t) equation. And it's the t that is the unknown (waiting time has an exponential distribution with parameter equal to the Poisson parameter).
