use probability of 3 claim is 0.1697

3. The surplus of an insurer follows a Lundberg process. Every year, premiums of 1 are received. A claim of size 3 occurs with probability (1500+)/10000 each year; otherwise there is no claim that year. (a) Calculate the probability of ruin within the first four years, starting with an initial surplus of 2. In this calculation, assume that ruin occurs if the surplus falls strictly below zero at one or more) of the time points (0, 1, 2, 3, 4). [8] (b) Let (u) denote the infinite-horizon ruin probability with initial surplus u. Derive a relationship expressing (u + 1) in terms of (u) and y(u - 2). [4] (e) In what follows, you may assume that y(u) takes the following form for integers u 20: (1 - 11)*2 - (1 - 12)4+2 Ad where -}