About

Alex Shkolnik is an Assistant Professor in the Department of Statistics and Applied Probability at the University of California, Santa Barbara. He is affiliated with the Mathematics major at UCSB College of Creative Studies. His academic role involves teaching courses related to probability, probability theory, and probability and combinatorics. Further details about his research focus, background, or key contributions are not provided on the page.

Research topics

• Statistics
• Computer Science
• Econometrics
• Mathematics
• Financial economics
• Economics
• Combinatorics
• Applied mathematics

Selected publications

• Exact Importance Sampling for a Linear Hawkes Process

  2025-12-07

  articleSenior author
  PublisherDOI

• Portfolio selection revisited

  Annals of Operations Research · 2024-11-04 · 3 citations

  articleOpen access1st authorCorresponding

  Abstract In 1952, Harry Markowitz formulated portfolio selection as a trade-off between expected, or mean, return and variance. This launched a massive research effort devoted to finding suitable inputs to mean-variance optimization. The estimation problem is high dimensional and a factor model is at the core of many attempts. A factor model can reduce the number of parameters that need to be estimated to a manageable size, but these parameters may incorporate substantial, hidden estimation error. Recent analysis elucidates the nature of this error, identifies a mechanism by which it can corrupt optimization and provides a method for its mitigation. We explore this analysis here by illustrating how to improve the volatility ratio of large optimized portfolios, leading to superior portfolio selection. $$^{*}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> </mml:mmultiscripts> </mml:math>

  PublisherOA PDFDOI

• The Quadratic Optimization Bias Of Large Covariance Matrices

  arXiv (Cornell University) · 2024-10-04 · 1 citations

  preprintOpen accessSenior author

  We describe a puzzle involving the interactions between an optimization of a multivariate quadratic function and a "plug-in" estimator of a spiked covariance matrix. When the largest eigenvalues (i.e., the spikes) diverge with the dimension, the gap between the true and the out-of-sample optima typically also diverges. We show how to "fine-tune" the plug-in estimator in a precise way to avoid this outcome. Central to our description is a "quadratic optimization bias" function, the roots of which determine this fine-tuning property. We derive an estimator of this root from a finite number of observations of a high dimensional vector. This leads to a new covariance estimator designed specifically for applications involving quadratic optimization. Our theoretical results have further implications for improving low dimensional representations of data, and principal component analysis in particular.

  PublisherOA PDFDOI

• Unbiased Simulation Estimators for Multivariate Jump-Diffusions

  arXiv (Cornell University) · 2021-11-02

  preprintOpen access

  We develop and analyze a class of unbiased Monte Carlo estimators for multivariate jump-diffusion processes with state-dependent drift, volatility, jump intensity and jump size. A change of measure argument is used to extend existing unbiased estimators for the inter-arrival diffusion to include state-dependent jumps. Under standard regularity conditions on the coefficient and target functions, we prove the unbiasedness and finite variance properties of the resulting jump-diffusion estimators. Numerical experiments illustrate the efficiency of our estimators.

  PublisherOA PDFDOI

• James-Stein estimation of the first principal component

  arXiv (Cornell University) · 2021-09-05

  preprintOpen access1st authorCorresponding

  The Stein paradox has played an influential role in the field of high dimensional statistics. This result warns that the sample mean, classically regarded as the "usual estimator", may be suboptimal in high dimensions. The development of the James-Stein estimator, that addresses this paradox, has by now inspired a large literature on the theme of "shrinkage" in statistics. In this direction, we develop a James-Stein type estimator for the first principal component of a high dimension and low sample size data set. This estimator shrinks the usual estimator, an eigenvector of a sample covariance matrix under a spiked covariance model, and yields superior asymptotic guarantees. Our derivation draws a close connection to the original James-Stein formula so that the motivation and recipe for shrinkage is intuited in a natural way.

  PublisherOA PDFDOI

• James–Stein estimation of the first principal component

  Stat · 2021 · 5 citations

  1st authorCorresponding
  • Mathematics
  • Statistics
  • Econometrics

  The Stein paradox has played an influential role in the field of high‐dimensional statistics. This result warns that the sample mean, classically regarded as the “usual estimator,” may be suboptimal in high dimensions. The development of the James–Stein estimator that addresses this paradox has by now inspired a large literature on the theme of “shrinkage” in statistics. In this direction, we develop a James–Stein‐type estimator for the first principal component of a high‐dimension and low‐sample size data set. This estimator shrinks the usual estimator, an eigenvector of a sample covariance matrix under a spiked covariance model, and yields superior asymptotic guarantees. Our derivation draws a close connection to the original James–Stein formula so that the motivation and recipe for shrinkage is intuited in a natural way.

  PublisherDOI

• Unbiased Simulation Estimators for Path Integrals of Diffusions

  2020-12-14

  article

  We develop and analyze Monte Carlo simulation estimators for path integrals of a multivariate diffusion with a general state-dependent drift and volatility. We prove that our estimators are unbiased and have finite variance by extending the regularity conditions of the parametrix method. The performance of our estimators is illustrated on numerical examples that highlight some applied problems for which our estimators apply.

  PublisherDOI

• Better Betas

  The Journal of Portfolio Management · 2020 · 6 citations

  • Computer Science
  • Econometrics
  • Statistics

  The authors introduce the data-driven Goldberg, Papanicolaou, and Shkolnik (GPS) adjustment for estimated betas, which leads to material improvements in the accuracy of weights and risk forecasts of minimum variance portfolios. Like the widely used Blume 2/3 rule and Vasicek adjustment developed in the 1970s, the GPS adjustment for estimated betas shrinks raw beta estimates toward one. Unlike its antecedents, the GPS adjustment operates on the dominant factor of a sample covariance matrix, and this adjustment adapts dynamically to varying levels of beta dispersion. The authors illustrate the power of the GPS adjustment in a simulation that is calibrated to calm and stressed market regimes. <b>TOPICS:</b>Factor-based models, portfolio construction, risk management, simulations <b>Key Findings</b> • Betas play a central role in determining optimized portfolios, and principal component analysis (PCA) is an effective tool to estimate betas. • More accurate PCA betas can be achieved with the Goldberg, Papanicolaou, and Shkolnik (GPS) adjustment, which is analogous to standard beta shrinkage adjustments applied to betas obtained from time-series regression. • Substantial improvements to the accuracy of minimum variance portfolio weights and risk forecasts may be realized when applying the GPS adjustment, which leads to better betas in any market regime.

  PublisherDOI

• The Dispersion Bias

  SIAM Journal on Financial Mathematics · 2017-01-01 · 1 citations

  preprintOpen accessSenior author

  We identify and correct excess dispersion in the leading eigenvector of a sample covariance matrix when the number of variables vastly exceeds the number of observations. Our correction is data-driven, and it materially diminishes the substantial impact of estimation error on weights and risk forecasts of minimum variance portfolios. We quantify that impact with a novel metric, the optimization bias, which has a positive lower bound prior to correction and tends to zero almost surely after correction. Our analysis sheds light on aspects of how estimation error corrupts an estimated covariance matrix and is transmitted to portfolios via quadratic optimization.

  PublisherDOI

Frequent coauthors

• Lisa R. Goldberg

  University of California, Berkeley

  6 shared

• Alex Papanicolaou

  5 shared

• Kay Giesecke

  Stanford University

  2 shared

• Guanting Chen

  2 shared

• Hubeyb Gurdogan

  2 shared

• Haim Bar

  University of Connecticut

  1 shared

• Simge Ulucam

  1 shared

• Alec N. Kercheval

  Florida State University

  1 shared