An insurance company starts with $1,000 dollars in its reserve. The company earns $100 per day which is added to the reserve every day. However, the insurance company is engaged in very risky business: each day, with probability $q=0.46$, the company may receive a claim, which will require it to pay $200 from its reserve the day it receives the claim.
Question 1: What is the probability that the insurance company will run out of its reserve eventually and be ruined?
(Hint: The situations of the gambler $G$ of [Gambler's Ruin] and the insurance company are not that different: at the end of each game, gambler $G$ is up or down a chip; and at the end of each day, the insurance company reserve is up or down by $100. When $G$ has no chips to play, $G$ is ruined; when the insurance company's reserve drops to $0, it is ruined.)
Question 2: What should be the company's reserve in order to make the probability of the company's ruin less than 0.1%?