Please Show Work

Consider an initial insurance portfolio of 10,000 independent automobile policies, each with a standard deviation of $200 and an expected loss of $200. Now suppose that this insurer also writes 500 independent fire insurance policies in order to diversify its line base. Each fire policy covers fairly large industrial risks, with an expected loss of $10,000 and a standard deviation of $12,000. a) Calculate the expected value and standard deviation of average loss per policy for the entire insurance portfolio. Show your calculations. b) Calculate Z statistic (which relates to the ruin probability), assuming the firm estimates that its reserves and surplus permit it to meet claims up to $900 per policy. Is the probability of ruin large or small based on this Z statistic? Show your calculations. c) Now assume that these policies are not independent; the correlation coefficient between any two auto policies is 0.05, and the correlation coefficient between any two fire policies is also 0.05; there is no correlation between auto and fire policies. Calculate the Z statistic again. Is the probability of ruin large or small based on this Z statistic? Show your calculations. Consider an initial insurance portfolio of 10,000 independent automobile policies, each with a standard deviation of $200 and an expected loss of $200. Now suppose that this insurer also writes 500 independent fire insurance policies in order to diversify its line base. Each fire policy covers fairly large industrial risks, with an expected loss of $10,000 and a standard deviation of $12,000. a) Calculate the expected value and standard deviation of average loss per policy for the entire insurance portfolio. Show your calculations. b) Calculate Z statistic (which relates to the ruin probability), assuming the firm estimates that its reserves and surplus permit it to meet claims up to $900 per policy. Is the probability of ruin large or small based on this Z statistic? Show your calculations. c) Now assume that these policies are not independent; the correlation coefficient between any two auto policies is 0.05, and the correlation coefficient between any two fire policies is also 0.05; there is no correlation between auto and fire policies. Calculate the Z statistic again. Is the probability of ruin large or small based on this Z statistic? Show your calculations