Problem 1. Consider a portfolio with random return rate R, where N possible re- alizations of the return rate (ri, j = 1,...,N) are available, whih are attained with probabilities Pj, j = 1, ... , N, respectively. (Q1.1) Formulate an optimization problem to calculate the following risk measure for this return rate: - E(return rate) + average value at risk at level a = 0.2 of the portfolio return rate) (Q1.2) Formulate the dual problem to the problem in Q1.1. What information does the dual problem provide? Problem 1. Consider a portfolio with random return rate R, where N possible re- alizations of the return rate (ri, j = 1,...,N) are available, whih are attained with probabilities Pj, j = 1, ... , N, respectively. (Q1.1) Formulate an optimization problem to calculate the following risk measure for this return rate: - E(return rate) + average value at risk at level a = 0.2 of the portfolio return rate) (Q1.2) Formulate the dual problem to the problem in Q1.1. What information does the dual problem provide