Portfolio problems with two levels decisionmakers: Optimal portfolio selection with pricing decisions on transaction costs Abstract   This paper presents novel bilevel leaderfollower portfolio selection problems in which the financial intermediary becomes a decisionmaker. This financial intermediary decides on the unit transaction costs for investing in some securities, maximizing its benefits, and the investor chooses his optimal portfolio, minimizing risk and ensuring a given expected return. Hence, transaction costs become decision variables in the portfolio problem, and two levels of decisionmakers are incorporated: the financial intermediary and the investor. These situations give rise to general Nonlinear Programming formulations in both levels of the decision process. We present different bilevel versions of the problem: financial intermediaryleader, investorleader, and social welfare; besides, their properties are analyzed. Moreover, we develop Mixed Integer Linear Programming formulations for some of the proposed problems and effective algorithms for some others. Finally, we report on some computational experiments performed on data taken from the Dow Jones Industrial Average, and analyze and compare the results obtained by the different models.

Global minimum variance portfolios under uncertainty: a robust optimization approach This paper presents new models which seek to optimize the first and second moments of asset returns without estimating expected returns. Motivated by the stability of optimal solutions computed by optimizing only the second moment and applying the robust optimization methodology which allows to incorporate the uncertainty in the optimization model itself, we extend and combine existing methodologies in order to define a method for computing relativerobust and absoluterobust minimum variance portfolios. For the relative robust strategy, where the maximum regret is minimized, regret is defined as the increase in the investment risk resulting from investing in a given portfolio instead of choosing the optimal portfolio of the realized scenario. The absolute robust strategy which minimizes the maximum risk was applied assuming the worstcase scenario over the whole uncertainty set. Across alternate time windows, results provide new evidence that the proposed robust minimum variance portfolios outperform nonrobust portfolios. Whether portfolio measurement is based on return, risk, regret or modified Sharpe ratio, results suggest that the robust methodologies are able to optimize the first and second moments without the need to estimate expected returns.