1. The claim cost of an insurance company follows a normal distribution with an expected value of $500 million and a standard deviation of $100 million. Based on the above, work on the following questions.

   1. In the graph, indicate the probability of insolvency of the insurer when it has an asset of $750 million. Please clearly label the axes.

   2. Show the probability of insolvency of the insurer after the insurer raises $100 million of new capital.

   3. Compute the probabilities of insolvency for the insurer when its total assets are respectively $750 and $850 million.

   4. What is the firms value at risk at the 1% level?

   5. Based on the distribution (the firms total asset is $750 million), show in the graph how the probability of insolvency changes when the insurer cedes a proportion of its liabilities to a reinsurer and simultaneously reinsurers a similar amount of business from another insurer with a similar, but uncorrelated book of business. Also explain your results in words.