Portfolio problems with two levels decision-makers: Optimal portfolio selection with pricing decisions on transaction costs

This paper presents novel bilevel leader-follower portfolio selection models in which the financial intermediary, that becomes a decision-maker, has to decide on the unit price transaction cost for investing in some securities, maximizing its benefits, and the investor has to choose his optimal portfolio, minimizing risk and ensuring a given expected return. One of the main contributions of this paper is that its models incorporate two level of decision-makers: the financial intermediary and the investor; which gives rise to general non linear problems in both levels of the decision process. We present different bilevel versions of the problem: bank-leader, investor-leader and social welfare models and analyze their properties. Moreover, we develop Mixed Integer Linear Programming formulations for some of the proposed models and efficient algorithms for some others. Finally, we report on some computational experiments performed on real data taken from the IBEX 35, the main benchmark stock exchange index of the Spanish stock market, and analyze and compare the results obtained by the different models.