[1] Bruder B, Gaussel N, Richard J, et al. Regularization of portfolio allocation [J]. SSRN Electronic Journal, 2013: 1-35.
[2] Costa Del Pozo G. Advances in Risk Parity Portfolio Optimization [M]. Toronto: University of Toronto, 2021.
[3] Ledoit O, Wolf M. Improved estimation of the covariance matrix of stock returns with an application to portfolio selection [J]. Journal of Empirical Finance, 2003, 10(5): 603-621.
[4] Ledoit O, Wolf M. A well-conditioned estimator for large-dimensional covariance matrices [J]. Journal of Multivariate Analysis, 2004, 88(2): 365-411.
[5] Ledoit O, Wolf M. Nonlinear shrinkage of the covariance matrix for portfolio selection: Markowitz meets goldilocks [J]. The Review of Financial Studies, 2017, 30(12): 4349-4388.
[6] Ledoit O, Wolf M. Quadratic shrinkage for large covariance matrices [J]. Bernoulli, 2022, 28(3): 1519-1547.
[7] Qian E. Risk parity portfolios: Efficient portfolios through true diversification [J]. Panagora Asset Management, 2005, 10(4): 513-524.
[8] Kolokolova O, Mattes A. How risky are low-risk hedge funds? [J]. Bankers, Markets, and Investors, Forthcoming, 2015: 1-32.
[9] Maillard S, Roncalli T, Teıletche J. The properties of equally weighted risk contribution portfolios [J]. The Journal of Portfolio Management, 2010, 36(4): 60-70.
[10] Maxey D. Are risk-parity funds a better strategy for diversification? [J]. The Wall Street Journal, 2015: 1-32.
[11] Costa G, Kwon R. Generalized risk parity portfolio optimization: An ADMM approach [J]. Journal of Global Optimization, 2020, 78: 207-238.
[12] Bai X, Scheinberg K, Tutuncu R. Least-squares approach to risk parity in portfolio selection [J]. Quantitative Finance, 2016, 16(3): 357-376.
[13] Mausser H, Romanko O. Computing equal risk contribution portfolios [J]. IBM Journal of Research and Development, 2014, 58(4): 1-12.
[14] Costa G, Kwon R. A robust framework for risk parity portfolios [J]. Journal of Asset Management, 2020, 21(5): 447-466.
[15] Costa G, Kwon R. Data-driven distributionally robust risk parity portfolio optimization [J]. Optimization Methods and Software, 2022, 37(5): 1876-1911.
[16] Bruder B, Kostyuchyk N, Roncalli T. Risk parity portfolios with skewness risk: An application to factor investing and alternative risk premia [EB/OL]. [2023-09-01]. arXiv: 2202.10721.
[17] Griveau-Billion T, Richard J C, Roncalli T. A fast algorithm for computing high-dimensional risk parity portfolios [EB/OL]. [2023-09-01]. arXiv: 1311.4057.
[18] Roncalli T, Weisang G. Risk parity portfolios with risk factors [J]. Quantitative Finance, 2016, 16(3): 377-388.
[19] Shannon C. A mathematical theory of communication [J]. The Bell System Technical Journal, 1984, 27(3): 379-423.
[20] Bera A, Park S. Optimal portfolio diversification using the maximum entropy principle [J]. Econometric Reviews, 2008, 27(4-6): 484-512.
[21] Dionısio A, Menezes R, Mendes D. Uncertainty analysis in financial markets: Can entropy be a solution [C]//Proceedings of the 10th Annual Workshop on Economic Heterogeneous Interacting Agents, 2005: 13-15.
[22] Simonelli M R. Indeterminacy in portfolio selection [J]. European Journal of Operational Research, 2005, 163(1): 170-176.
[23] Fernholz R, Karatzas I. Stochastic portfolio theory: An overview [J]. Handbook of Numerical Analysis, 2009, 15(89-167): 1180-91267.
[24] Ke J, Zhang C. Study on the optimization of portfolio based on entropy theory and meanvariance model [C]//2008 IEEE International Conference on Service Operations and Logistics, and Informatics, 2008, 2: 2668-2672.
[25] Zheng Y, Zhou M, Li G. Information entropy based fuzzy optimization model of electricity purchasing portfolio [C]//2009 IEEE Power & Energy Society General Meeting, 2009: 1-6.
[26] Yager R R. Measures of entropy and fuzziness related to aggregation operators [J]. Information Sciences, 1995, 82(3-4): 147-166.
[27] Wu J, Sun B, Liang C, et al. A linear programming model for determining ordered weighted averaging operator weights with maximal yager’s entropy [J]. Computers & Industrial Engineering, 2009, 57(3): 742-747.
[28] Yu J, Lee W, Chiou W. Diversified portfolios with different entropy measures [J]. Applied Mathematics and Computation, 2014, 241: 47-63.
[29] Rao C. Diversity: Its measurement, decomposition, apportionment and analysis [J]. Sankhya: The Indian Journal of Statistics, Series A, 1982: 1-22.
[30] Rao C, Nayak T. Cross entropy, dissimilarity measures, and characterizations of quadratic entropy [J]. IEEE Transactions on Information Theory, 1985, 31(5): 589-593.
[31] Koumou N B G. Rao’s quadratic entropy, risk management and portfolio theory [D]. Quebec City: Université Laval, 2017.
[32] Carmichael B, Koumou G, Moran K. Rao’s quadratic entropy and maximum diversification indexation [J]. Quantitative Finance, 2018, 18(6): 1017-1031.
[33] Koumou G B. Diversification and portfolio theory: A review [J]. Financial Markets and Portfolio Management, 2020, 34(3): 267-312.
[34] Booth D, Fama E. Diversification returns and asset contributions [J]. Financial Analysts Journal, 1992, 48(3): 26-32.
[35] Bouchey P, Nemtchinov V, Paulsen A, et al. Volatility harvesting: Why does diversifying and rebalancing create portfolio growth? [J]. The Journal of Wealth Management, 2012, 15(2): 26-35.
[36] Chambers D, Zdanowicz J. The limitations of diversification return [J]. The Journal of Portfolio Management, 2014, 40(4): 65-76.
[37] Maeso J, Martellini L. Maximizing an equity portfolio excess growth rate: A new form of smart beta strategy? [J]. Quantitative Finance, 2020, 20(7): 1185-1197.
[38] Brodie J, Daubechies I, Christine De Mol, et al. Sparse and stable markowitz portfolios [C]//Proceedings of the National Academy of Sciences, 2009, 106(30): 12267-12272.
[39] Zhao H, Kong L, Qi H. Optimal portfolio selections vian ‘1;2-norm regularization [J]. Computational Optimization and Applications, 2021, 80(3): 853-881.
[40] Ding C, Qi H D. An optimization study of diversification return portfolios [EB/OL]. [2023- 09-01]. arXiv: 2303.01657.
[41] DeMiguel V, Garlappi L, Uppal R. Optimal versus naive diversification: How inefficient is the 1=N portfolio strategy? [J]. The Review of Financial Studies, 2009, 22(5): 1915-1953.
[42] Behr P, Guettler A, Miebs F. On portfolio optimization: Imposing the right constraints [J]. Journal of Banking & Finance, 2013, 37(4): 1232-1242.
[43] Jagannathan R, Ma T S. Risk reduction in large portfolios: Why imposing the wrong constraints helps [J]. The Journal of Finance, 2003, 58(4): 1651-1683.
[44] DeMiguel V, Garlappi L, Nogales F J, et al. A generalized approach to portfolio optimization: Improving performance by constraining portfolio norms [J]. Management Science, 55(5): 798- 812, 2009.
[45] Tibshirani R. Regression shrinkage and selection via the lasso [J]. Journal of the Royal Statistical Society Series B: Statistical Methodology, 1996, 58(1): 267-288.
[46] Corsaro S, De Simone V. Adaptive ‘1-regularization for short-selling control in portfolio selection [J]. Computational Optimization and Applications, 2019, 72(2): 457-478.
[47] Fastrich B, Paterlini S, Winker P. Constructing optimal sparse portfolios using regularization methods [J]. Computational Management Science, 2015, 12(3): 417-434.
[48] Corsaro S, De Simone V, Marino Z. Fused Lasso approach in portfolio selection [J]. Annals of Operations Research, 2021, 299(1-2): 47-59.
[49] Kremer P J, Lee S, Bogdan M, et al. Sparse portfolio selection via the sorted ‘1-norm [J]. Journal of Banking & Finance, 2020, 110: 105687.
[50] Fan J Q, Zhang J J, Yu K. Vast portfolio selection with gross-exposure constraints [J]. Journal of the American Statistical Association, 2012, 107(498): 592-606.
[51] Lai Z R, Yang P Y, Fang L D, et al. Short-term sparse portfolio optimization based on alternating direction method of multipliers [J]. The Journal of Machine Learning Research, 2018, 19(1): 2547-2574.
[52] Yen Y M, Yen T J. Solving norm constrained portfolio optimization via coordinate-wise descent algorithms [J]. Computational Statistics & Data Analysis, 2014, 76: 737-759.
[53] Ho M, Sun Z, Xin J. Weighted elastic net penalized mean-variance portfolio design and computation [J]. SIAM Journal on Financial Mathematics, 2015, 6(1): 1220-1244.
[54] Dai Z F, Wen F H. A generalized approach to sparse and stable portfolio optimization problem [J]. Journal of Industrial & Management Optimization, 2018, 14(4): 1651-1666.
[55] Xing X, Hu J J, Yang Y N. Robust minimum variance portfolio with Lp-infinity constraints [J]. Journal of Banking & Finance, 2014, 46: 107-117.
[56] Shen W W, Wang J, Ma S Q. Doubly regularized portfolio with risk minimization [C] //Twenty-Eighth AAAI Conference on Artificial Intelligence, 2014.
[57] Chen J N, Dai G L, Zhang N. An application of sparse-group lasso regularization to equity portfolio optimization and sector selection [J]. Annals of Operations Research, 2020, 284: 243-262.
[58] Gao J J, Li D. Optimal cardinality constrained portfolio selection [J]. Operations Research, 2013, 61(3): 745-761.
[59] Xu F M, Wang G, Gao Y L. Nonconvex ‘ 12 regularization for sparse portfolio selection [J]. Pacific Journal of Optimization, 2014, 10(1): 163-176.
[60] Xu F M, Xu Z B, Xue H G. Sparse index tracking based on ‘ 12 model and algorithm [EB/OL]. [2023-09-01]. arXiv: 1506.05867.
[61] Luo Z Y, Yu X T, Xiu N H, et al. Closed-form solutions for short-term sparse portfolio optimization [J]. Optimization, 2022, 71(7): 1937-1953.
[62] Wu Z M, Xie G Y, Ge Z L, et al. Nonconvex multi-period mean-variance portfolio optimization [J]. Annals of Operations Research, 2023: 1-28.
[63] Fastrich B, Paterlini S, Winker P. Cardinality versus q-norm constraints for index tracking [J]. Quantitative Finance, 2014, 14(11): 2019-2032, 2014.
[64] Takeda A, Niranjan M, Gotoh J Y, et al. Simultaneous pursuit of out-of-sample performance and sparsity in index tracking portfolios [J]. Computational Management Science, 2013, 10: 21-49.
[65] Xu F M, Lu Z S, Xu Z B. An efficient optimization approach for a cardinality-constrained index tracking problem [J]. Optimization Methods and Software, 2016, 31(2): 258-271.
[66] Giuzio M. Genetic algorithm versus classical methods in sparse index tracking [J]. Decisions in Economics and Finance, 2017, 40(1-2): 243-256.
[67] Zhang C, Wang J J, Xiu N H. Robust and sparse portfolio model for index tracking [J]. Journal of Industrial & Management Optimization, 2019, 15(3): 1001-1015.
[68] Jiang T, Wang S, Zhang R C, et al. An inexact ‘2-norm penalty method for cardinality constrained portfolio optimization [J]. The Engineering Economist, 2019, 64(3): 289-297.
[69] Khodamoradi T, Salahi M, Najafi A R. Cardinality-constrained portfolio optimization with short selling and risk-neutral interest rate [J]. Decisions in Economics and Finance, 2021, 44: 197-214.
[70] Kim M J, Lee Y J, Kim J H, et al. Sparse tangent portfolio selection via semi-definite relaxation [J]. Operations Research Letters, 2016, 44(4): 540-543.
[71] Ruiz-Torrubiano R, Suárez A. A memetic algorithm for cardinality-constrained portfolio optimization with transaction costs [J]. Applied Soft Computing, 2015, 36: 125-142.
[72] Zhang J, Leung T, Aravkin A. A relaxed optimization approach for cardinality-constrained portfolios [C] //201918th European Control Conference, 2019: 2885-2892.
[73] Bhalla S, Melnekoff D T, Aleman A, et al. Patient similarity network of newly diagnosed multiple myeloma identifies patient subgroups with distinct genetic features and clinical implications [J]. Science Advances, 2021, 7(47): eabg9551.
[74] Varshney K R. Trustworthy machine learning and artificial intelligence [J]. XRDS: Crossroads, The ACM Magazine for Students, 2019, 25(3): 26-29.
[75] Perrin S, Roncalli T. Machine learning optimization algorithms and portfolio allocation [EB/OL]. [2023-09-01]. arXiv: 1909.10233.
[76] Joseph M, Kulkarni J, Mao J, et al. Locally private gaussian estimation [J]. Advances in Neural Information Processing Systems, 2019, 32: 1-27.
[77] Kamath G, Li J, Singhal V, et al. Privately learning high-dimensional distributions [C]//Conference on Learning Theory, 2019: 1853-1902.
[78] Karwa V, Vadhan S. Finite sample differentially private confidence intervals [EB/OL]. [2023- 09-01]. arXiv: 1711.03908.
[79] Wang D, Xu J H. Differentially private high dimensional sparse covariance matrix estimation [J]. Theoretical Computer Science, 2021, 865: 119-130.