Portfolio optimization — the systematic construction of asset allocations that balance return and risk — is a central problem in quantitative finance. Our research develops rigorous, computationally efficient methods that go well beyond the classical Markowitz mean-variance framework to address the real complexities of financial data. Core directions include risk parity portfolios , where risk contributions are equalized across assets; sparse portfolios for high-dimensional index tracking; high-order portfolios incorporating skewness and kurtosis for heavy-tailed return distributions; mean-reverting portfolios for statistical arbitrage; and online portfolio selection via adaptive algorithms for sequential investment under non-stationary markets. A parallel focus is robust statistical estimation of covariance matrices and distribution parameters from heavy-tailed, missing, or incomplete data. This research is supported by open-source Python and R packages at github.com/convexfi and by a dedicated textbook. Software GitHub software webpage Books Daniel P. Palomar, Portfolio Optimization: Theory and Application , Cambridge University Press, 2025. Konstantinos Benidis, Yiyong Feng, and Daniel P. Palomar, Optimization Methods for Financial Index Tracking: From Theory to Practice , Foundations and Trends® in Optimization, Now Publishers, 2018. [ pdf ] Yiyong Feng and Daniel P. Palomar, A Signal Processing Perspective on Financial Engineering , Foundations and Trends® in Signal Processing, Now Publishers, 2016. [ pdf ] Papers Runhao Shi and Daniel P. Palomar, “ SAOFTRL: A Novel Adaptive Algorithmic Framework for Enhancing Online Portfolio Selection ,” IEEE Trans. on Signal Processing , vol. 72, pp. 5291-5305, 2024. Runhao Shi, Jiaxi Ying, and and Daniel P. Palomar, “ Adaptive Passive-Aggressive Framework for Online Regression with Side Information ,” Advances in Neural Information Processing Systems (NeurIPS) , Vancouver, Canada, Dec. 2024. [25.8% acceptance rate] Xiwen Wang, Rui Zhou, Jiaxi Ying, and Daniel P. Palomar, “ Efficient and Scalable Parametric High-Order Portfolios Design via the Skew-t Distribution ,” IEEE Trans. on Signal Processing , vol. 71, pp. 3726-3740, 2023. Esa Ollila, Daniel P. Palomar, and Frédéric Pascal, “ Affine equivariant Tyler’s M-estimator applied to tail parameter learning of elliptical distributions ,” IEEE Signal Processing Letters , vol. 30, pp. 1017-1021, Aug. 2023. Shengjie Xiu, Xiwen Wang, and Daniel P. Palomar, “ A Fast Successive QP Algorithm for General Mean-Variance Portfolio Optimization ,” IEEE Trans. on Signal Processing , vol. 71, pp. 2713-2727, July 2023. Rui Zhou and Daniel P. Palomar, “ Solving High-Order Portfolios via Successive Convex Approximation Algorithms ,” IEEE Trans. on Signal Processing , vol. 69, pp. 892-904, Feb. 2021. Esa Ollila, Daniel P. Palomar, and Frédéric Pascal, “ Shrinking the Eigenvalues of M-estimators of Covariance Matrix ,” IEEE Trans. on Signal Processing , vol. 69, pp. 256-269, Jan. 2021. Rui Zhou, Junyan Liu, Sandeep Kumar, and Daniel P. Palomar, “ Student’s t VAR Modeling with Missing Data via Stochastic EM and Gibbs Sampling ,” IEEE Trans. on Signal Processing , vol. 68, pp. 6198-6211, Oct. 2020. Rui Zhou and Daniel P. Palomar, “ Understanding the Quintile Portfolio ,” IEEE Trans. on Signal Processing , vol. 68, pp. 4030-4040, July 2020. Linlong Wu, Yiyong Feng, and Daniel P. Palomar, “ General Sparse Risk Parity Portfolio Design via Successive Convex Optimization ,” Signal Processing , vol. 170, pp. 1-13, Dec. 2019. Junyan Liu and Daniel P. Palomar, “ Regularized Robust Estimation of Mean and Covariance Matrix for Incomplete Data ,” Signal Processing , vol. 165, pp. 278-291, July 2019. Junyan Liu, Sandeep Kumar, and Daniel P. Palomar, “ Parameter Estimation of Heavy-Tailed AR Model With Missing Data Via Stochastic EM ,” IEEE Trans. Signal Processing , vol. 67, no. 8, pp. 2159-2172, April 2019. [ R package imputeFin ] Ziping Zhao, Rui Zhou, and Daniel P. Palomar, “ Optimal Mean-Reverting Portfolio With Leverage Constraint for Statistical Arbitrage in Finance, ” IEEE Trans. on Signal Processing , vol. 67, no. 7, pp. 1681-1695, April 2019. Licheng Zhao and Daniel P. Palomar, “ A Markowitz Portfolio Approach to Options Trading ,” IEEE Trans. on Signal Processing , vol. 66, no. 16, pp. 4223-4238, Aug. 2018. Ziping Zhao and Daniel P. Palomar, “ Mean-Reverting Portfolio With Budget Constraint ,” IEEE Trans. on Signal Processing , vol. 66, no. 9, pp. 2342-2357, May 2018. Konstantinos Benidis, Yiyong Feng, and Daniel P. Palomar, “ Sparse Portfolios for High-Dimensional Financial Index Tracking ,” IEEE Trans. on Signal Processing , vol. 66, no. 1, pp. 155-170, Jan. 2018. [ R package sparseIndexTracking ] Ying Sun, Prabhu Babu, and Daniel P. Palomar, “ Robust Estimation of Structured Covariance Matrix for Heavy-Tailed Elliptical Distributions ,” IEEE Trans. on Signal Processing , vol. 64, no. 14, pp. 3576-3590, July 2016. [ Matlab code ] Yiyong Feng and Daniel P. Palomar, “ SCRIP: Successive Convex Optimization Methods for Risk Parity Portfolio Design ,” IEEE Trans. on Signal Processing , vol. 63, no. 19, pp. 5285-5300, Oct. 2015. [R package riskParityPortfolio ] Ying Sun, Prabhu Babu, and Daniel P. Palomar, “ Regularized Robust Estimation of Mean and Covariance Matrix Under Heavy-Tailed Distributions ,” IEEE Trans. on Signal Processing , vol. 63, no. 12, pp. 3096-3109, June 2015. [ Matlab code ] [ R package fitHeavyTail ] Junxiao Song, Prabhu Babu, and Daniel P. Palomar, “ Sparse Generalized Eigenvalue Problem via Smooth Optimization ,” IEEE Trans. on Signal Processing , vol. 63, no. 7, pp. 1627-1642, April 2015. [ Matlab code ] Yiyong Feng, Daniel P. Palomar, and Francisco Rubio, “ Robust Optimization of Order Execution ,” IEEE Trans. on Signal Processing , vol. 63, no. 4, pp. 907-920, Feb. 2015. Yang Yang, Francisco Rubio, Gesualdo Scutari, and Daniel P. Palomar, “ Multi-Portfolio Optimization: A Potential Game Approach ,” IEEE Trans. on Signal Processing , vol. 61, no. 22, pp. 5590-5602, Nov. 2013. Mengyi Zhang, Francisco Rubio, Daniel P. Palomar, and Xavier Mestre, “ Finite-Sample Linear Filter Optimization in Wireless Communications and Financial Systems ,” IEEE Trans. on Signal Processing , vol. 61, no. 20, pp. 5014-5025, Oct. 2013. Mengyi Zhang, Francisco Rubio, and Daniel P. Palomar, “ Improved Calibration of High-Dimensional Precision Matrices ,” IEEE Trans. on Signal Processing , vol. 61, no. 6, pp. 1509-1519, March 2013. Francisco Rubio, Xavier Mestre, and Daniel P. Palomar, “ Performance Analysis and Optimal Selection of Large Minimum-Variance Portfolios under Estimation Risk ,” IEEE Journal on Selected Topics in Signal Processing: Special Issue on Signal Processing Methods in Finance and Electronic Trading , vol. 6, no. 4, pp. 337-350, Aug. 2012.
