A Robust Knapsack Based Constrained Portfolio Optimization

Many portfolio optimization problems deal with allocation of assets which carry a relatively high market price. Therefore, it is necessary to determine the integer value of assets when we deal with portfolio optimization. In addition, one of the main concerns with most portfolio optimization is associated with the type of constraints considered in different models. In many cases, the resulted problem formulations do not yield in practical solutions. Therefore, it is necessary to apply some managerial decisions in order to make the results more practical. This paper presents a portfolio optimization based on an improved knapsack problem with the cardinality, floor and ceiling, budget, class, class limit and pre-assignment constraints for asset allocation. To handle the uncertainty associated with different parameters of the proposed model, we use robust optimization techniques. The model is also applied using some realistic data from US stock market. Genetic algorithm is also provided to solve the problem for some instances.

[1]  Frank J. Fabozzi,et al.  Focusing on the worst state for robust investing , 2015 .

[2]  Han-Lin Li,et al.  A distributed computation algorithm for solving portfolio problems with integer variables , 2008, Eur. J. Oper. Res..

[3]  Christos H. Papadimitriou,et al.  On the complexity of integer programming , 1981, JACM.

[4]  Xiaoxia Huang,et al.  Fuzzy chance-constrained portfolio selection , 2006, Appl. Math. Comput..

[5]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[6]  Melvyn Sim,et al.  Robust discrete optimization and network flows , 2003, Math. Program..

[7]  H. Kellerer,et al.  Introduction to NP-Completeness of Knapsack Problems , 2004 .

[8]  Bertrand Maillet,et al.  Global minimum variance portfolio optimisation under some model risk: A robust regression-based approach , 2015, Eur. J. Oper. Res..

[9]  Thomas Bäck,et al.  Evolutionary algorithms in theory and practice - evolution strategies, evolutionary programming, genetic algorithms , 1996 .

[10]  Amir Abbas Najafi,et al.  Robust goal programming for multi-objective portfolio selection problem , 2013 .

[11]  Maria Grazia Scutellà,et al.  Robust portfolio asset allocation and risk measures , 2013, Annals of Operations Research.

[12]  J. K. Lenstra,et al.  Computational complexity of discrete optimization problems , 1977 .

[13]  Carlos Artemio Coello-Coello,et al.  Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art , 2002 .

[14]  Ehram Safari,et al.  Robust optimization framework for cardinality constrained portfolio problem , 2012, Appl. Soft Comput..

[15]  Arkadi Nemirovski,et al.  Robust solutions of Linear Programming problems contaminated with uncertain data , 2000, Math. Program..

[16]  Justo Puerto,et al.  An algebraic approach to integer portfolio problems , 2010, Eur. J. Oper. Res..

[17]  Melvyn Sim,et al.  The Price of Robustness , 2004, Oper. Res..

[18]  Daniel Kuhn,et al.  Robust portfolio optimization with derivative insurance guarantees , 2011, Eur. J. Oper. Res..

[19]  Miguel A. Lejeune,et al.  An Exact Solution Approach for Portfolio Optimization Problems Under Stochastic and Integer Constraints , 2009, Oper. Res..

[20]  Melvyn Sim,et al.  Tractable Approximations to Robust Conic Optimization Problems , 2006, Math. Program..

[21]  Konstantinos P. Anagnostopoulos,et al.  Multiobjective evolutionary algorithms for complex portfolio optimization problems , 2011, Comput. Manag. Sci..

[22]  Yazid M. Sharaiha,et al.  Heuristics for cardinality constrained portfolio optimisation , 2000, Comput. Oper. Res..

[23]  Constantin Zopounidis,et al.  Robust multiobjective portfolio optimization: A minimax regret approach , 2017, Eur. J. Oper. Res..

[24]  Ken Darby-Dowman,et al.  Robust optimization and portfolio selection: The cost of robustness , 2011, Eur. J. Oper. Res..

[25]  Jih-Jeng Huang,et al.  A novel algorithm for uncertain portfolio selection , 2006, Appl. Math. Comput..

[26]  Daniela Favaretto,et al.  On the existence of solutions to the quadratic mixed-integer mean-variance portfolio selection problem , 2007, Eur. J. Oper. Res..

[27]  Chen Chen,et al.  Robust multiobjective portfolio with higher moments , 2018, Expert Syst. Appl..

[28]  A. Stuart,et al.  Portfolio Selection: Efficient Diversification of Investments , 1959 .

[29]  Ahmad Makui,et al.  A portfolio selection model based on the knapsack problem under uncertainty , 2019, PloS one.

[30]  Arkadi Nemirovski,et al.  Robust Convex Optimization , 1998, Math. Oper. Res..

[31]  Thomas Bäck,et al.  The zero/one multiple knapsack problem and genetic algorithms , 1994, SAC '94.

[32]  Panos Xidonas,et al.  Robust minimum variance portfolio optimization modelling under scenario uncertainty , 2017 .

[33]  Arkadi Nemirovski,et al.  Robust solutions of uncertain linear programs , 1999, Oper. Res. Lett..

[34]  Hao Di,et al.  Uncertain Portfolio Selection with Background Risk , 2014, 2014 International Conference on IT Convergence and Security (ICITCS).

[35]  Ralf Fröberg,et al.  An introduction to Gröbner bases , 1997, Pure and applied mathematics.

[36]  Dorothea Heiss-Czedik,et al.  An Introduction to Genetic Algorithms. , 1997, Artificial Life.

[37]  Allen L. Soyster,et al.  Technical Note - Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming , 1973, Oper. Res..

[38]  Mitsuo Gen,et al.  Genetic algorithms and engineering optimization , 1999 .

[39]  Dan Boneh,et al.  On genetic algorithms , 1995, COLT '95.

[40]  Xiang Li,et al.  A chance-constrained portfolio selection model with risk constraints , 2010, Appl. Math. Comput..

[41]  Cristiano Fernandes,et al.  An adaptive robust portfolio optimization model with loss constraints based on data-driven polyhedral uncertainty sets , 2016, Eur. J. Oper. Res..