1. An insurer's portfolio consists of a single possible claim. You are given the following information. The claim amount is uniformly distributed over (100, 500). The probability that the claim occurs after time t is e-0.1t for t > 0. The claim time and amount are independent. The insurer's initial surplus is 20. Premium income is received continuously at the rate of 40 per year. Determine the probability of ruin.
2. (a) A random variable G takes the value 1 with probability 6/7 and -1 with probability 1/7. Show that the adjustment coefficient of G is log(6).
(b) A random variable G takes the value 1 with probability 1/2 and 2 with probability 1/2. Show that the adjustment coefficient is ∞.