An insurance company has an initial surplus of 100 and premium loading factor of 20%. Assume that claims arrive according to a Poisson process with parameter =5 and the size of claims Xi are iid random variables with Xiexp(101). The time unit is 1 week. Assume that 1 month is 4 weeks. (a) Calculate the average number of claims on any given day, week and month. Let t>0 be an instance of time. Calculate the probability that at least one claim occurs within 5 days after t. Calculate also the probability that at least 2 claims occur within 5 days after t. (b) Let t=2 months. Calculate the mean and variance of S(t) and of U(t), where (S(r))r0 and (U(r))r0 are the aggregate claim process and the surplus process of the described model. (c) Derive an upper bound for the ultimate ruin probability using Lundberg's inequality. An insurance company has an initial surplus of 100 and premium loading factor of 20%. Assume that claims arrive according to a Poisson process with parameter =5 and the size of claims Xi are iid random variables with Xiexp(101). The time unit is 1 week. Assume that 1 month is 4 weeks. (a) Calculate the average number of claims on any given day, week and month. Let t>0 be an instance of time. Calculate the probability that at least one claim occurs within 5 days after t. Calculate also the probability that at least 2 claims occur within 5 days after t. (b) Let t=2 months. Calculate the mean and variance of S(t) and of U(t), where (S(r))r0 and (U(r))r0 are the aggregate claim process and the surplus process of the described model. (c) Derive an upper bound for the ultimate ruin probability using Lundberg's inequality