3. Suppose that the classical risk model applies. Let (V (t))>, denote the surplus process, that is, V(t) = v +ct - S(t), where the aggregate claims process (S(t))>, is a compound Poisson process with Pois- son parameter 1 = 3. Assume that the premium income rate per time unit is c = 12, where the time-unit is a day. (a) [9 marks] Assume that the individual claim amount is distributed according to a Pareto distribution X; ~ Pa(5,6). i. Check if the condition c > Am, on the premium income rate is satisfied. Why is this condition important? ii. Calculate the mean and the variance of S(5) iii. Calculate E(S(10) - S(5)S(5) , denote the surplus process, that is, V(t) = v +ct - S(t), where the aggregate claims process (S(t))>, is a compound Poisson process with Pois- son parameter 1 = 3. Assume that the premium income rate per time unit is c = 12, where the time-unit is a day. (a) [9 marks] Assume that the individual claim amount is distributed according to a Pareto distribution X; ~ Pa(5,6). i. Check if the condition c > Am, on the premium income rate is satisfied. Why is this condition important? ii. Calculate the mean and the variance of S(5) iii. Calculate E(S(10) - S(5)S(5)