Drawdown minimization in asset portfolio selection: MINLP models and efficient cross‐entropy algorithm

Abstract Portfolio management is an important research topic in finance and optimization. Drawdown as one of the measures in evaluating portfolios indicates the relative difference between the portfolio value in the current moment and its maximum value during a given time interval in the recent past. In this paper, first, the importance of this measure is discussed and then two mixed‐integer nonlinear programming (MINLP) models with the objectives of minimizing the expected drawdown and the maximum drawdown under real‐world constraints are presented. Due to the NP‐hardness of this problem, by utilizing the problem structure, an efficient cross‐entropy‐based algorithm is presented to solve it. An effective mechanism is suggested to calibrate the algorithm parameters. Computational results confirm the performance of the proposed algorithm from both solution quality and running time in comparison with MINLP solvers.