Use a sufficient number of samples ν from Theorem 4 for the sample approximation, (4.2), to ensure that the probabilistic constraint in (4.5) is satisfied with a confidence level of 1 − β = 0.99 with...

Use a sufficient number of samples ν from Theorem 4 for the sample approximation, (4.2), to ensure that the probabilistic constraint in (4.5) is satisfied with a confidence level of 1 − β = 0.99 with target reliability level, α = 0.95 , h = 0.95 , n = 125 , p = 0.01 for the probability of default on any single loan, and correlation coefficient ρ = 0.5 . (Since b is the only decision parameter to consider when all the loans are symmetric, you can assume the dimension to use in computing ν is one.) Find the minimum b∗ for 100 different sample problems. Verify the result in Theorem 4 empirically by constructing a sample of 10,000 sample portfolios and solving (4.5) for this large sample. What would you expect to happen if the problem is interpreted as making 125 separate decisions xj on the initial size of loan j ?