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

TL;DR

This paper introduces bilevel portfolio optimization models incorporating transaction costs as decision variables, analyzing different hierarchical decision structures and providing computational solutions with experiments on Dow Jones data.

Contribution

It develops novel bilevel models with transaction costs as decision variables and offers mixed-integer programming formulations and algorithms for solving them.

Findings

Different bilevel models analyzed and compared.

Effective algorithms developed for specific models.

Computational experiments demonstrate model performance.

Abstract

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.