Skip to main content
Log in

A brief review of portfolio optimization techniques

  • Published:
Artificial Intelligence Review Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Alpaydin E (2020) Introduction to machine learning. MIT Press, Cambridge

    MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Anagnostopoulos KP, Mamanis G (2011) Multiobjective evolutionary algorithms for complex portfolio optimization problems. CMS 8(3):259–279

    Article  MathSciNet  Google Scholar 

  • Artzner P, Delbaen F, Eber JM, Heath D (1999) Coherent measures of risk. Math Financ 9(3):203–228

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    MATH  Google Scholar 

  • Aversa P, Haefliger S, Reza DG (2017) Building a winning business model portfolio. MIT Sloan Manag Rev 58(4):49–54

    Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • Ban GY, El Karoui N, Lim AE (2018) Machine learning and portfolio optimization. Manag Sci 64(3):1136–1154

    Article  Google Scholar 

  • Bauer E, Kohavi R (1999) An empirical comparison of voting classification algorithms: bagging, boosting, and variants. Mach Learn 36(1):105–139

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Bäuerle N, Rieder U (2011) Markov decision processes with applications to finance. Springer, New York

    Book  MATH  Google Scholar 

  • Best MJ, Hlouskova J (2000) The efficient frontier for bounded assets. Math Methods Oper Res 52(2):195–212

    Article  MathSciNet  MATH  Google Scholar 

  • Betancourt C, Chen WH (2021) Deep reinforcement learning for portfolio management of markets with a dynamic number of assets. Expert Syst Appl 164:114002

    Article  Google Scholar 

  • Borisov AV (2011) The wonham filter under uncertainty: a game-theoretic approach. Automatica 47(5):1015–1019

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Cai X, Teo KL, Yang X, Zhou XY (2004) Minimax portfolio optimization: empirical numerical study. J Oper Res Soc 55(1):65–72

    Article  MATH  Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • Chaouki A, Hardiman S, Schmidt C, Sérié E, De Lataillade J (2020) Deep deterministic portfolio optimization. J Financ Data Sci 6:16–30

    Article  Google Scholar 

  • Chen JM (2016) Sortino, omega, kappa: the algebra of financial asymmetry. Postmodern portfolio theory. Springer, New York, pp 79–105

    Chapter  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Cooper RG, Edgett SJ, Kleinschmidt EJ (2001) Portfolio management. Pegasus, New York

    Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • Crama Y, Schyns M (2003) Simulated annealing for complex portfolio selection problems. Eur J Oper Res 150(3):546–571

    Article  MATH  Google Scholar 

  • Cura T (2009) Particle swarm optimization approach to portfolio optimization. Nonlinear Anal Real World Appl 10(4):2396–2406

    Article  MathSciNet  MATH  Google Scholar 

  • Das S, Markowitz H, Scheid J, Statman M (2010) Portfolio optimization with mental accounts. J Financ Quant Anal 45(2):311–334

    Article  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1(4):28–39

    Article  Google Scholar 

  • Dowd K (2007) Measuring market risk. Wiley, New York

    Google Scholar 

  • 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

    Google Scholar 

  • Eckhardt R (1987) Stan ulam, john von neumann, and the monte carlo method. Los Alamos Sci 15(30):131–136

    MathSciNet  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Eiben AE, Smith JE et al (2003) Introduction to evolutionary computing, vol 53. Springer, New York

    Book  MATH  Google Scholar 

  • El-Shorbagy MA, Hassanien AE (2018) Particle swarm optimization from theory to applications. Int J Rough Sets Data Anal 5(2):1–24

    Article  Google Scholar 

  • Feldstein MS (1969) Mean-variance analysis in the theory of liquidity preference and portfolio selection. Rev Econ Stud 36(1):5–12

    Article  Google Scholar 

  • Fernández A, Gómez S (2007) Portfolio selection using neural networks. Comput Oper Res 34(4):1177–1191

    Article  MATH  Google Scholar 

  • 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

    Article  MathSciNet  Google Scholar 

  • Friedman JH, Hall P (2007) On bagging and nonlinear estimation. J Stat Plan Inference 137(3):669–683

    Article  MathSciNet  MATH  Google Scholar 

  • Galai D, Mark R, Crouhy M (2001) Risk management: comprehensive chapters on market, credit, and operational risk. McGraw-Hill, New York

    Google Scholar 

  • Galai D, Mark R, Crouhy M (2001) Risk management: comprehensive chapters on market, credit, and operational risk. McGraw-Hill, New York

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    MathSciNet  MATH  Google Scholar 

  • Holton GA (2003) Value-at-risk. Academic Press, Washington

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Konno H, Yamazaki H (1991) Mean-absolute deviation portfolio optimization model and its applications to tokyo stock market. Manage Sci 37(5):519–531

    Article  Google Scholar 

  • Krokhmal P, Palmquist J, Uryasev S (2002) Portfolio optimization with conditional value-at-risk objective and constraints. J Risk 4:43–68

    Article  Google Scholar 

  • Kuo SY, Chou YH (2017) Entanglement-enhanced quantum-inspired tabu search algorithm for function optimization. IEEE Access 5:13236–13252

    Article  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • Li B, Sun Y, Aw G, Teo KL (2019) Uncertain portfolio optimization problem under a minimax risk measure. Appl Math Model 76:274–281

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Lin J (1976) Multiple-objective problems: pareto-optimal solutions by method of proper equality constraints. IEEE Trans Autom Control 21(5):641–650

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Google Scholar 

  • Lwin KT, Qu R, MacCarthy BL (2017) Mean-var portfolio optimization: a nonparametric approach. Eur J Oper Res 260(2):751–766

    Article  MathSciNet  MATH  Google Scholar 

  • Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188(2):1567–1579

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • 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

    Google Scholar 

  • Markowitz HM, Todd GP (2000) Mean-variance analysis in portfolio choice and capital markets, vol 66. Wiley, New York

    Google Scholar 

  • McMahon D (2007) Quantum computing explained. Wiley, New York

    Book  MATH  Google Scholar 

  • McNeil AJ, Frey R, Embrechts P (2015) Quantitative risk management: concepts, techniques and tools-revised edition. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Mirjalili S (2019) Genetic algorithm. Evolutionary algorithms and neural networks. Springer, New York, pp 43–55

    Chapter  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Montiel O, Rubio Y, Olvera C, Rivera A (2019) Quantum-inspired acromyrmex evolutionary algorithm. Sci Rep 9(1):1–10

    Article  Google Scholar 

  • Moody J, Saffell M (2001) Learning to trade via direct reinforcement. IEEE Trans Neural Networks 12(4):875–889

    Article  Google Scholar 

  • Moon Y, Yao T (2011) A robust mean absolute deviation model for portfolio optimization. Comput Oper Res 38(9):1251–1258

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • Nielsen MA, Chuang IL (2001) Quantum computation and quantum information. Phys Today 54(2):60

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Orus R, Mugel S, Lizaso E (2019) Quantum computing for finance: overview and prospects. Rev Phys 4(100):028

    Google Scholar 

  • 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

    Article  MathSciNet  Google Scholar 

  • 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

    Article  Google Scholar 

  • Rämö H (2002) Doing things right and doing the right things time and timing in projects. Int J Project Manag 20(7):569–574

    Article  Google Scholar 

  • Ranković V, Drenovak M, Urosevic B, Jelic R (2016) Mean-univariate garch var portfolio optimization: actual portfolio approach. Comput Oper Res 72:83–92

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    MathSciNet  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Rockafellar RT, Uryasev S (2002) Conditional value-at-risk for general loss distributions. J Bank Financ 26(7):1443–1471

    Article  Google Scholar 

  • Rockafellar RT, Uryasev S et al (2000) Optimization of conditional value-at-risk. J Risk 2:21–42

    Article  Google Scholar 

  • Roll R (1992) A mean/variance analysis of tracking error. J Portfolio Manag 18(4):13–22

    Article  Google Scholar 

  • Saad HM, Chakrabortty RK, Elsayed S, Ryan MJ (2021) Quantum-inspired genetic algorithm for resource-constrained project-scheduling. IEEE Access 9:38488–38502

    Article  Google Scholar 

  • Saboia JLM (1977) Autoregressive integrated moving average (arima) models for birth forecasting. J Am Stat Assoc 72(358):264–270

    Article  Google Scholar 

  • 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

    MATH  Google Scholar 

  • 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

    Chapter  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Schmidhuber J, Hochreiter S et al (1997) Long short-term memory. Neural Comput 9(8):1735–1780

    Article  Google Scholar 

  • 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

    MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • Soleymani F, Paquet E (2020) Financial portfolio optimization with online deep reinforcement learning and restricted stacked autoencoder-deepbreath. Expert Syst Appl 156(113):456

    Google Scholar 

  • Soleymani F, Paquet E (2021) Deep graph convolutional reinforcement learning for financial portfolio management-deeppocket. Expert Syst Appl 182(115):127

    Google Scholar 

  • 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

    MATH  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Wolsey LA, Nemhauser GL (1999) Integer and combinatorial optimization, vol 55. Wiley, New York

    MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Google Scholar 

  • Yang X (2006) Improving portfolio efficiency: a genetic algorithm approach. Comput Econ 28(1):1

    Article  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    MathSciNet  MATH  Google Scholar 

  • Yin G, Liu R, Zhang Q (2002) Recursive algorithms for stock liquidation: a stochastic optimization approach. SIAM J Optim 13(1):240–263

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Young TW (1991) Calmar ratio: a smoother tool. Futures 20(1):40

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Siddhartha Bhattacharyya.

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.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10462-022-10273-7

Keywords

Navigation