Question 3. The Great Manuf (GM) insurance company expects an average of 1000 claims in automobile insurance in the next year, with the actual number of claims being random and well described by a Poisson distribution. The value of each claim is also uncertain, independent of all other claims, following a normal distribution with a mean of HK$30,000 and a standard deviation of $9,000. GM has HK$36 million of capital, which is split into two parts. The first part is the reserve capital needed to pay claims over the next year. The other part will be invested in short-term bonds, which give a random return that is equally likely to be any value from 5% to 8% annually. If the reserve capital turns out to be less than the total value of claims for the year, GM has to borrow enough money, at a cost of 10% of the amount borrowed, to make up the difference. GM would like to find a capital allocation that maximizes the expected amount of cash they have left at the end of the year. (a) Suppose GM allocates half of the available capital to the reserved capital. Formulate a spreadsheet model and use ASPE to perform 1,000 trials of a computer simulation on a spreadsheet. [Note: please include the model in the sheet named Q3a in file Q3.xlsx.] (10 marks) Your answer: Expected amount of cash left = Question 3. The Great Manuf (GM) insurance company expects an average of 1000 claims in automobile insurance in the next year, with the actual number of claims being random and well described by a Poisson distribution. The value of each claim is also uncertain, independent of all other claims, following a normal distribution with a mean of HK$30,000 and a standard deviation of $9,000. GM has HK$36 million of capital, which is split into two parts. The first part is the reserve capital needed to pay claims over the next year. The other part will be invested in short-term bonds, which give a random return that is equally likely to be any value from 5% to 8% annually. If the reserve capital turns out to be less than the total value of claims for the year, GM has to borrow enough money, at a cost of 10% of the amount borrowed, to make up the difference. GM would like to find a capital allocation that maximizes the expected amount of cash they have left at the end of the year. (a) Suppose GM allocates half of the available capital to the reserved capital. Formulate a spreadsheet model and use ASPE to perform 1,000 trials of a computer simulation on a spreadsheet. [Note: please include the model in the sheet named Q3a in file Q3.xlsx.] (10 marks) Your answer: Expected amount of cash left =