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This paper presents novel bilevel leader-follower portfolio selectionproblems in which the financial intermediary becomes a decision-maker. Thisfinancial intermediary decides on the unit transaction costs for investing insome securities, maximizing its benefits, and the investor chooses his optimalportfolio, minimizing risk and ensuring a given expected return. Hence,transaction costs become decision variables in the portfolio problem, and twolevels of decision-makers are incorporated: the financial intermediary and theinvestor. These situations give rise to general Nonlinear Programmingformulations in both levels of the decision process. We present differentbilevel versions of the problem: financial intermediary-leader,investor-leader, and social welfare; besides, their properties are analyzed.Moreover, we develop Mixed Integer Linear Programming formulations for some ofthe proposed problems and effective algorithms for some others. Finally, wereport on some computational experiments performed on data taken from the DowJones Industrial Average, and analyze and compare the results obtained by thedifferent models.

Portfolio problems with two levels decision-makers: Optimal portfolio  selection with pricing decisions on transaction costs. Extended version and  complete risk profiles analysis