A general insurer writes 1000 niche personal lines motor vehicle policies at the beginning of the year. The policies are independent. There are no withdrawals. The policies are renewable for a maximum term of 3 years, where premiums are payable annually in advance. Claims are paid at the end of the year. Individual claim amounts follow a Gamma distribution, with Alpha = 1000 and Lambda = 0.1. Each policy has a 0.02 probability of claiming each year. Premiums per year are priced as follows: * Covers expected aggregate claims for the year * Covers an expense loading of 0.1 of the annual premium * Includes a profit loading of 0.1 of the standard deviation of aggregate claims for the year Force of interest is 0.05 per annum. The insurer has starting capital equal to 20% of the expected aggregate claims for the first year. You assume that actual experience equals expected experience each year. 1. Determine the mean and standard deviation of the aggregate claims for each year. 2. Determine the premiums charged at the beginning of each year. 3. Determine the Balance Sheets at times 0, 1, 2, 3 in years. 4. Assuming that aggregate claims are approximately Normal, use Q1 and Q3 to determine the probabilities of ruin for each year over the lifetime of the policies. The regulator demands ruin probabilities of no more than 0.5% for each year. 5. Determine the additional amount of capital that needs to be injected at the beginning of each year.