1. A special insurance company has a single contract. There can be at most one claim, and the probability that a claim does not occur by time t is 1/(1 + t). If a claim occurs, the amount is 100 with probability 0.6 or 200 with probability 0.4. Premiums are paid continuously at the rate of 20 per year. The company begins with an initial surplus of 60. What is the probability of eventual ruin?
2. Consider again the game of flipping a fair coin, winning 1 for heads, starting with an initial surplus of 3. The gambler decides to stop at time 4 or whenever two consecutive heads come up, if earlier. What is the expected surplus at the end of the game?