  This paper presents novel bilevel leader-follower portfolio selection
problems in which the financial intermediary becomes a decision-maker. 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 decision-makers 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 intermediary-leader,
investor-leader, 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.
