Abstract
Portfolio optimization has always been a challenging proposition in finance and management. Portfolio optimization facilitates in selection of portfolios in a volatile market situation. In this paper, different classical, statistical and intelligent approaches employed for portfolio optimization and management are reviewed. A brief study is performed to understand why portfolio is important for any organization and how recent advances in machine learning and artificial intelligence can help portfolio managers to take right decisions regarding allotment of portfolios. A comparative study of different techniques, first of its kind, is presented in this paper. An effort is also made to compile classical, intelligent, and quantum-inspired techniques that can be employed in portfolio optimization.
Similar content being viewed by others
References
Aboussalah AM, Lee CG (2020) Continuous control with stacked deep dynamic recurrent reinforcement learning for portfolio optimization. Expert Syst Appl 140(112):891
Achiam J, Knight E, Abbeel P (2019) Towards characterizing divergence in deep q-learning. arXiv preprint arXiv:1903.08894
Agrawal R, Kaur B, Agarwal P (2021) Quantum inspired particle swarm optimization with guided exploration for function optimization. Appl Soft Comput 102(107):122
Almahdi S, Yang SY (2017) An adaptive portfolio trading system: A risk-return portfolio optimization using recurrent reinforcement learning with expected maximum drawdown. Expert Syst Appl 87:267–279
Alpaydin E (2020) Introduction to machine learning. MIT Press, Cambridge
Alvarez-Alvarado MS, Alban-Chacón FE, Lamilla-Rubio EA, Rodríguez-Gallegos CD, Velásquez W (2021) Three novel quantum-inspired swarm optimization algorithms using different bounded potential fields. Sci Rep 11(1):1–22
Anagnostopoulos KP, Mamanis G (2011) The mean-variance cardinality constrained portfolio optimization problem: an experimental evaluation of five multiobjective evolutionary algorithms. Expert Syst Appl 38(11):14208–14217
Anagnostopoulos KP, Mamanis G (2011) Multiobjective evolutionary algorithms for complex portfolio optimization problems. CMS 8(3):259–279
Artzner P, Delbaen F, Eber JM, Heath D (1999) Coherent measures of risk. Math Financ 9(3):203–228
Ausiello G, Crescenzi P, Gambosi G, Kann V, Marchetti-Spaccamela A, Protasi M (2012) Complexity and approximation: combinatorial optimization problems and their approximability properties. Springer, New York
Aversa P, Haefliger S, Reza DG (2017) Building a winning business model portfolio. MIT Sloan Manag Rev 58(4):49–54
Babaei G, Giudici P (2021) Explainable artificial intelligence for crypto asset allocation. Available at SSRN 3977051
Babaei S, Sepehri MM, Babaei E (2015) Multi-objective portfolio optimization considering the dependence structure of asset returns. Eur J Oper Res 244(2):525–539
Bahmani B, Moseley B, Vattani A, Kumar R, Vassilvitskii S (2012) Scalable k-means++. arXiv preprint arXiv:1203.6402
Bai L, Zhang K, Shi H, An M, Han X (2020) Project portfolio resource risk assessment considering project interdependency by the fuzzy bayesian network. Complexity. https://doi.org/10.1155/2020/5410978
Ban GY, El Karoui N, Lim AE (2018) Machine learning and portfolio optimization. Manag Sci 64(3):1136–1154
Bauer E, Kohavi R (1999) An empirical comparison of voting classification algorithms: bagging, boosting, and variants. Mach Learn 36(1):105–139
Bauer R, Hoevenaars R, Steenkamp T (2006) Asset liability management. The oxford handbook of pensions and retirement income. Oxford University Press, Oxford, pp 417–440
Bäuerle N, Rieder U (2011) Markov decision processes with applications to finance. Springer, New York
Best MJ, Hlouskova J (2000) The efficient frontier for bounded assets. Math Methods Oper Res 52(2):195–212
Betancourt C, Chen WH (2021) Deep reinforcement learning for portfolio management of markets with a dynamic number of assets. Expert Syst Appl 164:114002
Borisov AV (2011) The wonham filter under uncertainty: a game-theoretic approach. Automatica 47(5):1015–1019
Brogan AJ, Stidham S Jr (2008) Non-separation in the mean-lower-partial-moment portfolio optimization problem. Eur J Oper Res 184(2):701–710
Bruder B, Gaussel N, Richard JC, Roncalli T (2013) Regularization of portfolio allocation. Available at SSRN 2767358
Bühlmann P, Yu B (2002) Analyzing bagging. Ann Stat 30(4):927–961
Cai X, Teo KL, Yang X, Zhou XY (2004) Minimax portfolio optimization: empirical numerical study. J Oper Res Soc 55(1):65–72
Cappart Q, Moisan T, Rousseau LM, Prémont-Schwarz I, Cire A (2020) Combining reinforcement learning and constraint programming for combinatorial optimization. arXiv preprint arXiv:2006.01610
Cesarone F, Scozzari A, Tardella F (2011) Portfolio selection problems in practice: a comparison between linear and quadratic optimization models. arXiv preprint arXiv:1105.3594
Chang TJ, Meade N, Beasley JE, Sharaiha YM (2000) Heuristics for cardinality constrained portfolio optimisation. Comput Oper Res 27(13):1271–1302
Chaouki A, Hardiman S, Schmidt C, Sérié E, De Lataillade J (2020) Deep deterministic portfolio optimization. J Financ Data Sci 6:16–30
Chen JM (2016) Sortino, omega, kappa: the algebra of financial asymmetry. Postmodern portfolio theory. Springer, New York, pp 79–105
Chen W, Tan S, Yang D (2011) Worst-case var and robust portfolio optimization with interval random uncertainty set. Expert Syst Appl 38(1):64–70
Chiang HP, Chou YH, Chiu CH, Kuo SY, Huang YM (2014) A quantum-inspired tabu search algorithm for solving combinatorial optimization problems. Soft Comput 18(9):1771–1781
Choi HK (2018) Stock price correlation coefficient prediction with arima-lstm hybrid model. arXiv preprint arXiv:1808.01560
Chou YH, Kuo SY, Chen CY, Chao HC (2014) A rule-based dynamic decision-making stock trading system based on quantum-inspired tabu search algorithm. IEEE Access 2:883–896
Chou YH, Kuo SY, Kuo C (2014) A dynamic stock trading system based on a multi-objective quantum-inspired tabu search algorithm. In: 2014 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp 112–119. IEEE
Chou YH, Yang YJ, Chiu CH (2011) Classical and quantum-inspired tabu search for solving 0/1 knapsack problem. In: 2011 IEEE International Conference on Systems, Man, and Cybernetics, pp 1364–1369. IEEE
Chu SC, Tsai PW, Pan JS (2006) Cat swarm optimization. In: Pacific Rim International Conference on Artificial Intelligence, pp 854–858. Springer
Coloni A, Dorigo M, Maniezzo V (1996) Ant system: optimization by a colony of cooperating agent. IEEE Trans Syst Man Cybern Part B 26(1):29–41
Cooper RG, Edgett SJ, Kleinschmidt EJ (2001) Portfolio management. Pegasus, New York
Corne DW, Knowles JD, Oates MJ (2000) The pareto envelope-based selection algorithm for multiobjective optimization. In: International Conference on Parallel Problem Solving from Nature, pp 839–848. Springer
Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20(3):273–297
Crama Y, Schyns M (2003) Simulated annealing for complex portfolio selection problems. Eur J Oper Res 150(3):546–571
Cura T (2009) Particle swarm optimization approach to portfolio optimization. Nonlinear Anal Real World Appl 10(4):2396–2406
Das S, Markowitz H, Scheid J, Statman M (2010) Portfolio optimization with mental accounts. J Financ Quant Anal 45(2):311–334
Davis L (1991) Handbook of genetic algorithms. CumInCAD
Deng GF, Lin WT (2010) Ant colony optimization for markowitz mean-variance portfolio model. In: International Conference on Swarm, Evolutionary, and Memetic Computing, pp 238–245. Springer
Derbeko P, El-Yaniv R, Meir R (2002) Variance optimized bagging. In: European Conference on Machine Learning, pp 60–72. Springer
Derigs U, Nickel NH (2003) Meta-heuristic based decision support for portfolio optimization with a case study on tracking error minimization in passive portfolio management. OR Spectrum 25(3):345–378
Derigs U, Nickel NH (2004) On a local-search heuristic for a class of tracking error minimization problems in portfolio management. Ann Oper Res 131(1):45–77
Dey S, Bhattacharyya S, Maulik U (2018) Quantum-inspired automatic clustering technique using ant colony optimization algorithm. In: Quantum-Inspired Intelligent Systems for Multimedia Data Analysis, pp 27–54. IGI Global
DiVincenzo DP (1998) Quantum gates and circuits. Proc R Soc Lond Ser A 454(1969):261–276
Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1(4):28–39
Dowd K (2007) Measuring market risk. Wiley, New York
Drucker H, Burges CJ, Kaufman L, Smola A, Vapnik V et al (1997) Support vector regression machines. Adv Neural Inf Process Syst 9:155–161
Eckhardt R (1987) Stan ulam, john von neumann, and the monte carlo method. Los Alamos Sci 15(30):131–136
Eckstein S, Kupper M (2019) Computation of optimal transport and related hedging problems via penalization and neural networks. Appl Math Optim 83(2):639–667
Eiben AE, Smith JE et al (2003) Introduction to evolutionary computing, vol 53. Springer, New York
El-Shorbagy MA, Hassanien AE (2018) Particle swarm optimization from theory to applications. Int J Rough Sets Data Anal 5(2):1–24
Feldstein MS (1969) Mean-variance analysis in the theory of liquidity preference and portfolio selection. Rev Econ Stud 36(1):5–12
Fernández A, Gómez S (2007) Portfolio selection using neural networks. Comput Oper Res 34(4):1177–1191
Forqandoost Haqiqi K, Kazemi T (2011) Ant colony optimization approach to portfolio optimization. Tohid, Ant Colony Optimization Approach to Portfolio Optimization (August 26, 2011)
Frank M, Wolfe P et al (1956) An algorithm for quadratic programming. Naval R Logist Q 3(1–2):95–110
Friedman JH, Hall P (2007) On bagging and nonlinear estimation. J Stat Plan Inference 137(3):669–683
Galai D, Mark R, Crouhy M (2001) Risk management: comprehensive chapters on market, credit, and operational risk. McGraw-Hill, New York
Galai D, Mark R, Crouhy M (2001) Risk management: comprehensive chapters on market, credit, and operational risk. McGraw-Hill, New York
García-Galicia M, Carsteanu AA, Clempner JB (2019) Continuous-time reinforcement learning approach for portfolio management with time penalization. Expert Syst Appl 129:27–36
Glover F, Laguna M (1998) Tabu search. In: Handbook of combinatorial optimization, pp 2093–2229. Springer
Goodman R, Thornton M, Strasser S, Sheppard JW (2016) Micpso: A method for incorporating dependencies into discrete particle swarm optimization. In: 2016 IEEE Symposium Series on Computational Intelligence (SSCI), pp 1–8. IEEE
Guan D, Hipel KW, Fang L, Guo P (2014) Assessing project portfolio risk based on bayesian network. In: 2014 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp 1546–1551. IEEE
Guan Dj, Guo P (2014) Constructing interdependent risks network of project portfolio based on bayesian network. In: 2014 International Conference on Management Science & Engineering 21th Annual Conference Proceedings, pp 1587–1592. IEEE
Guennoun Z, Hamza F et al (2012) Stocks portfolio optimization using classification and genetic algorithms. Appl Math Sci 6(94):4673–4684
Guntsch M, Middendorf M (2003) Solving multi-criteria optimization problems with population-based aco. In: International Conference on Evolutionary Multi-Criterion Optimization, pp 464–478. Springer
Han KH, Kim JH (2002) Quantum-inspired evolutionary algorithm for a class of combinatorial optimization. IEEE Trans Evol Comput 6(6):580–593
Han KH, Park KH, Lee CH, Kim JH (2001) Parallel quantum-inspired genetic algorithm for combinatorial optimization problem. In: Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No. 01TH8546), vol 2, pp 1422–1429. IEEE
Haugh MB, Lo AW (2001) Computational challenges in portfolio management. Comput Sci Eng 3(3):54–59
Haykin S (2010) Neural networks and learning machines, 3/E. Pearson Education India
Hayre L (2002) Salomon Smith Barney guide to mortgage-backed and asset-backed securities, vol 105. Wiley, New York
He Y, Aranha C (2020) Solving portfolio optimization problems using moea/d and levy flight. arXiv preprint arXiv:2003.06737
Hibiki N (2001) Multi-period stochastic programming models using simulated paths for strategic asset allocation. J Oper Res Soc Japan 2(44):193
Holton GA (2003) Value-at-risk. Academic Press, Washington
Ito K, Kunisch K (2008) Lagrange multiplier approach to variational problems and applications. SIAM
Jeffery M, Leliveld I (2004) Best practices in it portfolio management. MIT Sloan Manag Rev 45(3):41
Jiang Z, Xu D, Liang J (2017) A deep reinforcement learning framework for the financial portfolio management problem. arXiv preprint arXiv:1706.10059
Jorion P (1997) Value at risk: the new benchmark for controlling market risk. Irwin Professional Pub
Jorion P (2007) Value at risk: the new benchmark for managing financial risk. The McGraw-Hill Companies Inc, New York
Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Tech. Rep, Citeseer
Karatzas I, Zhao X (2001) Bayesian adaptive portfolio optimization. Option pricing, interest rates and risk management, pp 632–669
Karimkashi S, Kishk AA (2010) Invasive weed optimization and its features in electromagnetics. IEEE Trans Antennas Propag 58(4):1269–1278
Karmakar S, Dey A, Saha I (2017) Use of quantum-inspired metaheuristics during last two decades. In: 2017 7th International Conference on Communication Systems and Network Technologies (CSNT), pp 272–278. IEEE
Kaye P, Laflamme R, Mosca M, et al. (2007) An introduction to quantum computing. Oxford University Press on Demand
Kennedy J, Eberhart R (1942) Particle swarm optimization in: Neural networks. In: Proceedings IEEE International Conference on 1995, pp 1942–1948
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95-International Conference on Neural Networks, vol. 4, pp 1942–1948. IEEE
Konno H, Koshizuka T (2005) Mean-absolute deviation model. Iie. Transactions 37(10):893–900
Konno H, Yamazaki H (1991) Mean-absolute deviation portfolio optimization model and its applications to tokyo stock market. Manage Sci 37(5):519–531
Krokhmal P, Palmquist J, Uryasev S (2002) Portfolio optimization with conditional value-at-risk objective and constraints. J Risk 4:43–68
Kuo SY, Chou YH (2017) Entanglement-enhanced quantum-inspired tabu search algorithm for function optimization. IEEE Access 5:13236–13252
Kuo SY, Kuo C, Chou YH (2013) Dynamic stock trading system based on quantum-inspired tabu search algorithm. In 2013 IEEE Congress on Evolutionary Computation, pp 1029–1036. IEEE
Ładyżyński P, Żbikowski K, Grzegorzewski P (2013) Stock trading with random forests, trend detection tests and force index volume indicators. In: International Conference on Artificial Intelligence and Soft Computing, pp 441–452. Springer
Lazimy R (1982) Mixed-integer quadratic programming. Math Program 22(1):332–349
Lee Y, Kim MJ, Kim JH, Jang JR, Chang Kim W (2020) Sparse and robust portfolio selection via semi-definite relaxation. J Oper Res Soc 71(5):687–699
Li B, Sun Y, Aw G, Teo KL (2019) Uncertain portfolio optimization problem under a minimax risk measure. Appl Math Model 76:274–281
Li D, Sun X, Wang J (2006) Optimal lot solution to cardinality constrained mean-variance formulation for portfolio selection. Math Financ 16(1):83–101
Li Y (2017) Deep reinforcement learning: an overview. arXiv preprint arXiv:1701.07274
Li Y, Heng B, Zhou S, Chen R, Liu S (2012) A novel aco algorithm based on average entropy for real estate portfolio optimization. J Theor Appl Inf Technol 45(2):502–507
Liang Z, Chen H, Zhu J, Jiang K, Li Y (2018) Adversarial deep reinforcement learning in portfolio management. arXiv preprint arXiv:1808.09940
Lim AE, Shanthikumar JG, Vahn GY (2011) Conditional value-at-risk in portfolio optimization: coherent but fragile. Oper Res Lett 39(3):163–171
Lin J (1976) Multiple-objective problems: pareto-optimal solutions by method of proper equality constraints. IEEE Trans Autom Control 21(5):641–650
Lin YC, Chen CT, Sang CY, Huang SH (2022) Multiagent-based deep reinforcement learning for risk-shifting portfolio management. Appl Soft Comput 123(108):894
Lwin KT, Qu R, MacCarthy BL (2017) Mean-var portfolio optimization: a nonparametric approach. Eur J Oper Res 260(2):751–766
Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188(2):1567–1579
Mansini R, Ogryczak W, Speranza MG (2015) Portfolio optimization with transaction costs. In: Linear and Mixed Integer Programming for Portfolio Optimization, pp 47–62. Springer
Mansini R, Speranza MG (1999) Heuristic algorithms for the portfolio selection problem with minimum transaction lots. Eur J Oper Res 114(2):219–233
Mariano CE, Morales EM (1999) Moaq an ant-q algorithm for multiple objective optimization problems. In: Proceedings of the 1st Annual Conference on Genetic and Evolutionary Computation, vol 1, pp 894–901
Markowitz H (1959) Portfolio selection, efficent diversification of investments. Wiley, New York
Markowitz HM, Todd GP (2000) Mean-variance analysis in portfolio choice and capital markets, vol 66. Wiley, New York
McMahon D (2007) Quantum computing explained. Wiley, New York
McNeil AJ, Frey R, Embrechts P (2015) Quantitative risk management: concepts, techniques and tools-revised edition. Princeton University Press, Princeton
Mirjalili S (2019) Genetic algorithm. Evolutionary algorithms and neural networks. Springer, New York, pp 43–55
Mnih V, Kavukcuoglu K, Silver D, Rusu AA, Veness J, Bellemare MG, Graves A, Riedmiller M, Fidjeland AK, Ostrovski G et al (2015) Human-level control through deep reinforcement learning. Nature 518(7540):529–533
Mohsin SA, Darwish SM, Younes A (2021) Qiaco: a quantum dynamic cost ant system for query optimization in distributed database. IEEE Access 9:15833–15846
Montiel O, Rubio Y, Olvera C, Rivera A (2019) Quantum-inspired acromyrmex evolutionary algorithm. Sci Rep 9(1):1–10
Moody J, Saffell M (2001) Learning to trade via direct reinforcement. IEEE Trans Neural Networks 12(4):875–889
Moon Y, Yao T (2011) A robust mean absolute deviation model for portfolio optimization. Comput Oper Res 38(9):1251–1258
Mugel S, Kuchkovsky C, Sanchez E, Fernandez-Lorenzo S, Luis-Hita J, Lizaso E, Orus R (2020) Dynamic portfolio optimization with real datasets using quantum processors and quantum-inspired tensor networks. arXiv preprint arXiv:2007.00017
Mulvey JM (2001) Multi-stage optimization for long-term investors. In: Quantitative Analysis In Financial Markets: Collected Papers of the New York University Mathematical Finance Seminar (Volume III), pp 66–85. World Scientific
Narayanan A, Moore M (1996) Quantum-inspired genetic algorithms. In: Proceedings of IEEE International Conference on Evolutionary Computation, pp 61–66. IEEE
Nawrocki DN (1992) The characteristics of portfolios selected by n-degree lower partial moment. Int Rev Financ Anal 1(3):195–209
Nielsen MA, Chuang IL (2001) Quantum computation and quantum information. Phys Today 54(2):60
NYSE NASDAQ, A (2003) New york stock exchange (nyse), nasdaq, and amex data from january 1996 to september 2003 in the crsp/compustat merged database (Jan’1996–Sep’2003)
Oh KJ, Kim TY, Min S (2005) Using genetic algorithm to support portfolio optimization for index fund management. Expert Syst Appl 28(2):371–379
Orus R, Mugel S, Lizaso E (2019) Quantum computing for finance: overview and prospects. Rev Phys 4(100):028
Park K, Jung HG, Eom TS, Lee SW (2022) Uncertainty-aware portfolio management with risk-sensitive multiagent network. In: IEEE Transactions on Neural Networks and Learning Systems
Passino KM (2002) Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Syst Mag 22(3):52–67
Pedersen M (2014) Portfolio optimization and monte carlo simulation. Available at SSRN 2438121
Rabiner L, Juang B (1986) An introduction to hidden Markov models. IEEE ASSP Mag 3(1):4–16
Rämö H (2002) Doing things right and doing the right things time and timing in projects. Int J Project Manag 20(7):569–574
Ranković V, Drenovak M, Urosevic B, Jelic R (2016) Mean-univariate garch var portfolio optimization: actual portfolio approach. Comput Oper Res 72:83–92
Ray J, Bhattacharyya S (2015) Value-at-risk based portfolio allocation using particle swarm optimization. Int J Comput Sci Eng (E-ISSN: 2347-2693) 3: 1–9
Ray J, Bhattacharyya S (2017) Particle swarm optimization technique for optimizing conditional value-at-risk based portfolio. Int J Comput Sci Eng 5(2)
Rebentrost P, Lloyd S (2018) Quantum computational finance: quantum algorithm for portfolio optimization. arXiv preprint arXiv:1811.03975
Reyes-Sierra M, Coello CC et al (2006) Multi-objective particle swarm optimizers: a survey of the state-of-the-art. Int J Comput Intell Res 2(3):287–308
Rezani M, Hertono G, Handari B (2020) Implementation of iterative k-means-+ and ant colony optimization (aco) in portfolio optimization problem. In: AIP Conference Proceedings, vol 2242, p 030022. AIP Publishing LLC
Rockafellar RT (1970) Conjugate convex functions in optimal control and the calculus of variations. J Math Anal Appl 32(1):174–222
Rockafellar RT, Uryasev S (2002) Conditional value-at-risk for general loss distributions. J Bank Financ 26(7):1443–1471
Rockafellar RT, Uryasev S et al (2000) Optimization of conditional value-at-risk. J Risk 2:21–42
Roll R (1992) A mean/variance analysis of tracking error. J Portfolio Manag 18(4):13–22
Saad HM, Chakrabortty RK, Elsayed S, Ryan MJ (2021) Quantum-inspired genetic algorithm for resource-constrained project-scheduling. IEEE Access 9:38488–38502
Saboia JLM (1977) Autoregressive integrated moving average (arima) models for birth forecasting. J Am Stat Assoc 72(358):264–270
Salahi M, Daemi M, Lotfi S, Jamalian A (2014) Pso and harmony search algorithms for cardinality constrained portfolio optimization problem. Adv Model Optim 16(3):559–573
Samuelson PA (1975) The fundamental approximation theorem of portfolio analysis in terms of means, variances and higher moments. Stochastic optimization models in finance. Elsevier, Amsterdam, pp 215–220
Schlichtkrull M, Kipf TN, Bloem P, Berg Rvd, Titov I, Welling M (2018) Modeling relational data with graph convolutional networks. In: European Semantic Web Conference, pp 593–607. Springer
Schlottmann F, Seese D (2004) A hybrid heuristic approach to discrete multi-objective optimization of credit portfolios. Comput Stat Data Anal 47(2):373–399
Schmidhuber J, Hochreiter S et al (1997) Long short-term memory. Neural Comput 9(8):1735–1780
Schulman J, Wolski F, Dhariwal P, Radford A, Klimov O (2017) Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347
Seng H (1992-1997) Weekly price from hang seng in Hong Kong, dax 100 in Germany, FTSE 100 in UK, s &p 100 in USA and Nikkei in Japan
Shenoy C, Shenoy PP (2000) Bayesian network models of portfolio risk and return. The MIT Press, Cambridge
Shi S, Li J, Li G, Pan P (2019) A multi-scale temporal feature aggregation convolutional neural network for portfolio management. In: Proceedings of the 28th ACM International Conference on Information and Knowledge Management, pp 1613–1622
Shi S, Li J, Li G, Pan P, Chen Q, Sun Q (2022) Gpm: a graph convolutional network based reinforcement learning framework for portfolio management. Neurocomputing 498:14–27
Soleymani F, Paquet E (2020) Financial portfolio optimization with online deep reinforcement learning and restricted stacked autoencoder-deepbreath. Expert Syst Appl 156(113):456
Soleymani F, Paquet E (2021) Deep graph convolutional reinforcement learning for financial portfolio management-deeppocket. Expert Syst Appl 182(115):127
SP500: One year data from s &p 500 from January 2016 to January 2017 (Jan’2016–Jan’2017)
Sutton RS, Barto AG (2018) Reinforcement learning: an introduction. MIT Press, Cambridge
Talbi H, Draa A, Batouche M (2006) A novel quantum-inspired evolutionary algorithm for multi-sensor image registration. Int Arab J Inf Technol 3(1):9–15
Tan Y, Zhu Y (2010) Fireworks algorithm for optimization. In: International Conference in Swarm Intelligence, pp 355–364. Springer
Van Veldhuizen DA, Lamont GB (1998) Multiobjective evolutionary algorithm research: a history and analysis. Tech. Rep., Citeseer
Vazquez E, Clempner JB (2020) Customer portfolio model driven by continuous-time markov chains: an l 2 Lagrangian regularization method. Econ Comput Econ Cybern Stud Res 54(2)
Whitley D (1994) A genetic algorithm tutorial. Stat Comput 4(2):65–85
Wolsey LA, Nemhauser GL (1999) Integer and combinatorial optimization, vol 55. Wiley, New York
Wu ME, Syu JH, Lin JCW, Ho JM (2021) Portfolio management system in equity market neutral using reinforcement learning. Appl Intell 51(11):8119–8131
Zl Wu, Zhang A, Li Ch, Sudjianto A (2008) Trace solution paths for svms via parametric quadratic programming. Data Mining Using Matrices and Tensors, KDD Worskshop
Xu C (2003) Soft approach for solving hard optimization problems. In: Proceedings of of the Fall National Conference of Japan Society for Management Information, pp 74–77
Xu C, Ng P (2006) A soft approach for hard continuous optimization. Eur J Oper Res 173(1):18–29
Xu C, Wang J, Shiba N (2007) Multistage portfolio optimization with var as risk measure. Int J Innov Comput Inf Control 3(3):709–724
Yang X (2006) Improving portfolio efficiency: a genetic algorithm approach. Comput Econ 28(1):1
Yang XS (2009) Firefly algorithms for multimodal optimization. In: International Symposium on Stochastic Algorithms, pp 169–178. Springer
Yang XS (2010) A new metaheuristic bat-inspired algorithm. In: Nature Inspired Cooperative Strategies for Optimization (NICSO 2010), pp 65–74. Springer
Yang Y, Xu DL (2017) A methodology for assessing the effect of portfolio management on npd performance based on bayesian network scenarios. Expert Syst 34(2):e12186
Yang Z, Yin G, Zhang Q (2015) Mean-variance type controls involving a hidden markov chain: models and numerical approximation. IMA J Math Control Inf 32(4):867–888
Yin G, Liu R, Zhang Q (2002) Recursive algorithms for stock liquidation: a stochastic optimization approach. SIAM J Optim 13(1):240–263
Yin X, Ni Q, Zhai Y (2015) A novel pso for portfolio optimization based on heterogeneous multiple population strategy. In: 2015 IEEE Congress on Evolutionary Computation (CEC), pp 1196–1203. IEEE
Young MR (1998) A minimax portfolio selection rule with linear programming solution. Manag Sci 44(5):673–683
Young TW (1991) Calmar ratio: a smoother tool. Futures 20(1):40
Yu P, Lee JS, Kulyatin I, Shi Z, Dasgupta S (2019) Model-based deep reinforcement learning for dynamic portfolio optimization. arXiv preprint arXiv:1901.08740
Yusoff Y, Ngadiman MS, Zain AM (2011) Overview of nsga-ii for optimizing machining process parameters. Procedia Eng 15:3978–3983
Zhou A, Qu BY, Li H, Zhao SZ, Suganthan PN, Zhang Q (2011) Multiobjective evolutionary algorithms: a survey of the state of the art. Swarm Evol Comput 1(1):32–49
Zhu H, Wang Y, Wang K, Chen Y (2011) Particle swarm optimization (pso) for the constrained portfolio optimization problem. Expert Syst Appl 38(8):10161–10169
Zitzler E, Laumanns M, Thiele L (2001) Spea2: improving the strength pareto evolutionary algorithm. TIK-Report 103
Zouache D, Nouioua F, Moussaoui A (2016) Quantum-inspired firefly algorithm with particle swarm optimization for discrete optimization problems. Soft Comput 20(7):2781–2799
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Gunjan, A., Bhattacharyya, S. A brief review of portfolio optimization techniques. Artif Intell Rev 56, 3847–3886 (2023). https://doi.org/10.1007/s10462-022-10273-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10462-022-10273-7