Portfolio Optimization

Risk parity portfolio

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.