Mie377 Financial Optimization Models Exam 2019

This study source was downloaded by 100000859819779 from CourseHero.com on 04-08-2023 11:09:24 GMT -05:00https://www.coursehero.com/file/188717147/MIE377S-2019-FINANCIALOPTIMIZATIONMODELS-E-1pdf/ M1E377 Financial Optimization Models Final Exam - Winter 2019 Exam Time and Date: 06:30 PM / 23-Apr-2019 Note: This is a closed book, closed notes exam except for both sides of a 3-by-5 inch handwritten notecard. A non-programmable and non-financial calculator is allowed. Please show all your work. Partial marks will only be awarded if your work is clear and neat. Useful information: d b Inverse ofa2x2matn abx:A= A- = 1 C d ad bc c a Inverse of std. normal CDF at 95%: 1.96 Square root of inverse chi square CDF at 95% with 2 dof: 2.50 Problem 1 (14 points) Consider the following problem max y(x+1) x,y s.t. x+y22, x>0, y>0. Use the KKT conditions to solve this problem. Hint: Consider the subset of scenarios that may satisfy the KKT conditions, and choose your solution from there. Problem 2 (14 points) Consider the following problem max (i.ln(x%)) s.t; x>O for i=1,...,n. Find a solution for x, in terms of P, n and i. Justify your answer. 1This study source was downloaded by 100000859819779 from CourseHero.com on 04-08-2023 11:09:24 GMT -05:00https://www.coursehero.com/file/188717147/MIE377S-2019-FINANCIALOPTIMIZATIONMODELS-E-1pdf/Problem 5 (12 points) Consider