This Week in Mathematics


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Entries for this week: 4

Monday March 09, 2026

PhD Dissertation Defense
Long-Only Minimum Variance Optimization: Analytical Foundations, Asymptotic Estimation, and the Enhanced Active-Set Algorithm
- Ololade Sowunmi, FSU
Time: 3:00 pm Room: LOV 204
Abstract/Desc: This dissertation develops a unified theoretical and algorithmic framework for the long-only mini- mum variance (LOMV) portfolio problem under a one-factor covariance structure. The work begins by deriving an explicit closed-form solution to the classical LOMV problem under this structure, providing a complete analytical characterization of the optimal weights and the associated active set. Building on this foundation, the dissertation investigates the impact of factor-loading esti- mation in high dimensions. It establishes that the dispersion bias inherent in the PCA estimator leads to persistent over-diversification, and suggests that the James–Stein eigenvector shrinkage (JSE) estimator produces a strictly smaller asymptotic deviation from the true active-set propor- tion. The analysis further shows that PCA systematically underestimates portfolio risk, whereas the JSE estimator—evaluated through the Variance Forecast Ratio—does not exhibit this bias. The final part of the dissertation introduces the Enhanced Active-Set Algorithm for the One-Factor Model and proves that, under non-degeneracy assump- tions, the algorithm recovers the optimal active set exactly. Numerical experiments demonstrate that the proposed algorithm reliably identifies the true solution and outperforms standard opti- mization routines in both accuracy and stability. Collectively, these results provide new insight into the geometry, estimation sensitivity, and computational structure of long-only minimum variance portfolios, particularly in high-dimensional regimes.

Tuesday March 10, 2026

- Nir Gadish, UPenn
Time: 3:05PM Room: LOV 232

Wednesday March 11, 2026

Biomathematics Journals
Operating Principles of Interconnected Feedback Loops Driving Cell Fate Transitions
- Philip Asare, FSU
Time: 5:00 Room: Dirac Library

Thursday March 12, 2026

Financial Math
- Gökçe Dayanıklı, University of Illinois Urbana-Champaign
Time: 3.05 Room: LOV 231

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This Week in Mathematics