Professor of Mathematics & Director, Financial Mathematics

Alec Kercheval

I am a professor in the Department of Mathematics at Florida State University and Director of the Financial Mathematics MS and PhD programs. I am also an Affiliated Researcher with the Consortium for Data Analytics in Risk at UC Berkeley. My research spans financial mathematics, mathematical economics, dynamical systems, and geometric analysis.

Brief CV ORCID Google Scholar Financial Math Program

Scholarship

Research Areas

Shrinkage Estimators for Portfolio Risk

Developing improved covariance estimation methods for high-dimensional, low sample-size settings critical to portfolio optimization. Jointly with Lisa Goldberg, Alex Shkolnik, and Hubeyb Gurdogan.

covarianceportfolio theoryrandom matrix

High-Frequency Limit Order Book Dynamics

Statistical and machine-learning models of intra-day limit order book behavior and its connection to derivative pricing. Encompasses forecasting, stochastic modeling, and market microstructure.

HFTmachine learningmarket microstructure

Credit Risk Modeling

Structural jump-threshold frameworks for credit risk, multi-dimensional default models, and stochastic intensity approaches to default dependency and correlation.

credit riskstochastic processes

Agent-Based Pricing & Dynamical Systems

Endogenous asset pricing dynamics from heterogeneous, boundedly rational agent models. Earlier work on differentiable dynamics and geometric measure theory.

dynamical systemsagent-based modelsfractal geometry

Scholarship

Publications and Preprints

Books

2010

Lectures on Financial Mathematics: Discrete Asset Pricing

with G. Anderson · Synthesis Lectures on Mathematics and Statistics, Springer

Articles

2025

Understanding the Long-Only Minimum Variance Portfolio

with Nick Gunther and Ololade Sowunmi · arxiv.org/abs/2603.07692 · 24 pp.

2025

James-Stein Shrinkage for High Dimensional Eigenvectors

with Lisa Goldberg and Hubeyb Gurdogan · Proceedings of the 2025 Joint Statistical Meetings · 7 pp.

2025

Portfolio Optimization via Strategy-specific Eigenvector Shrinkage

with Lisa Goldberg and Hubeyb Gurdogan · Finance and Stochastics, vol. 25, 665–706

2024

Portfolio Selection Revisited

with Lisa Goldberg, Alex Shkolnik, Hubeyb Gurdogan, Haim Bar · Annals of Operations Research, vol. 346, 137–155

2023

James-Stein for the Leading Eigenvector

with Lisa Goldberg · Proc. National Academy of Sciences, vol. 120, no. 2 · 9 pp.

2022

Multiple Anchor Point Shrinkage for the Sample Covariance Matrix

with Hubeyb Gurdogan · SIAM Journal on Financial Mathematics, vol. 13, no. 3, 1112–1143

2022

Pricing and Hedging Options Conditional on Market Activity

with Navid Salehy and Nima Salehy · Journal of Mathematical Finance, vol. 12, no. 1, 1–19

2021

Multiple Anchor Point Shrinkage for the Sample Covariance Matrix (Extended Version)

with Hubeyb Gurdogan · arXiv:2109.00148v2 [q-fin.CP] · 60 pp.

2018

Modeling Credit Risk in the Jump Threshold Framework

with C.-Y. Chiu · Applied Mathematical Finance · 23 pp.

2016

A Structural Jump Threshold Framework for Credit Risk

with P. Garreau · SIAM Journal on Financial Mathematics, vol. 7, no. 1, 642–673

2015

Modeling High-Frequency Limit Order Book Dynamics with Support Vector Machines

with Y. Zhang · Quantitative Finance, vol. 15, no. 8, 1315–1329

2014

Complex Dynamics in Equilibrium Asset Pricing Models with Boundedly Rational, Heterogeneous Agents

with P. Beaumont and Y. Guan · Complexity, vol. 19, no. 3, 38–55

2013

Asset Market Dynamics in Equilibrium Models with Heterogeneous Agents: Analytical Results

with P. Beaumont and A. Culham · Advances in Economics and Business, vol. 1, no. 2, 49–56

2012

A Generalized Birth-Death Stochastic Model for High-Frequency Order Book Dynamics

with H. Huang · Quantitative Finance, vol. 12, no. 4, 547–557

2012

Risk Forecasting with GARCH, Skewed t Distributions, and Multiple Timescales

with Y. Liu · Chapter 7 in Handbook of Modeling High-Frequency Data in Finance, Wiley, 163–218

2010

Portfolio Optimization for t and Skewed t Returns

with W. Hu · Quantitative Finance, vol. 10, no. 1, 91–105

2009

The Skewed t Distribution for Portfolio Credit Risk

with W. Hu · Advances in Econometrics, vol. 22, Elsevier, 55–83

2009

Optimal intervention in the foreign exchange market when interventions affect market dynamics

with J. Moreno · arXiv:0909.1142 · 28 pp

2008

On Rebonato and Jackel's Parametrization Method for Finding Nearest Correlation Matrices

International Journal of Pure and Applied Mathematics, vol. 45, no. 3, 383–390

2007

Risk Management with Generalized Hyperbolic Distributions

with W. Hu · Proceedings, Fourth IASTED International Conference on Financial Engineering and Applications, ACTA Press, 19–24

2006

Optimal Covariances in Risk Model Aggregation

Proceedings, Third IASTED International Conference on Financial Engineering and Applications, ACTA Press, 30–35

2005

On the Aggregation of Local Risk Models for Global Risk Management

with G. Anderson, L. Goldberg, G. Miller, and K. Sorge · Journal of Risk, 8, no. 1, 25–40

2005

t-Statistics for Weighted Means in Credit Risk Modelling

with L. Goldberg and K. Lee · Journal of Risk Finance, 6, no. 4, 349–365

2003

Modelling Credit Risk: Currency Dependence in Global Credit Markets

with L. Goldberg and L. Breger · Journal of Portfolio Management, vol. 29, no. 2, Winter 2003

2002

Examining Market Influence on Credit Risk

with L. Goldberg and L. Breger · Risk Management for Investors (supplement to Risk Magazine), 15, no. 6, S21–S22

2002

Denjoy Minimal Sets Are Far from Affine

Ergodic Theory and Dynamical Systems, vol. 22, 1803–1812 · Erratum · arXiv:1004.1363v1

2001

Currency Dependence in Global Credit Markets

with L. Goldberg and L. Breger · Security Analysts Journal, 39, no. 10, 61–74

1999

Cantor Sets, Binary Trees, and Lipschitz Circle Homeomorphisms

with B. Tandy · Michigan Mathematical Journal, vol. 46, 29–38

1999

Denjoy's Theorem with Exponents

Proceedings of the American Mathematical Society, vol. 127, no. 10, 3111–3118

1996

Wandering Domains and Invariant Conformal Structures for Mappings of the 2-Torus

with D. Sullivan · Annales Academiæ Scientiarum Fennicæ, Series A I Mathematica, vol. 21, 51–68

1996

On Sets of Critical Values in the Real Line

with S. Bates · Duke Mathematical Journal, vol. 83, 399–413

1994

The Zygmund Morse-Sard Theorem

Journal of Geometric Analysis, 4, no. 3, 403–424

1994

Conformal Irregularity for Denjoy Diffeomorphisms of the 2-Torus

with J. Velling · Rocky Mountain Journal of Mathematics, 24, no. 2, 655–671

1992

The Gauss-Green Theorem for Fractal Boundaries

with J. Harrison · Duke Mathematical Journal, 67, 575–588

1991

A C^1+∞ Function with an Interval of Critical Values

Indiana University Mathematics Journal, 40, no. 4, 1483–1488

1991

Geometric Integration on Fractal Curves in the Plane

with J. Harrison · Indiana University Mathematics Journal, 40, no. 2, 567–594

1991

Critical Sets in the Plane

with C. Pugh · Michigan Mathematical Journal, 38, 441–459

1991

An Area Approach to Wandering Domains for Smooth Surface Endomorphisms

Ergodic Theory and Dynamical Systems, 11, 181–187

1989

Functions Not Constant on Fractal Quasi-Arcs of Critical Points

Proceedings of the American Mathematical Society, 106, 397–406

1988

Continued Fractions and Differentiability of Functions

American Mathematical Monthly, 95, 639–643

1986

A Critical Set with Non-Null Image Has Large Hausdorff Dimension

Transactions of the American Mathematical Society, 296, 367–376

1984

Complex Roots Made Visible

with B. Lotto · College Journal of Mathematics, 15, 248–249

Invited Articles

2019

10 Ancient Rules for Giving a Conference/Seminar/Research Talk in Mathematics

Notices of the AMS, 66, no. 10, 1650–1651

2012

Book Review: Financial Economics: A Concise Introduction to Classical and Behavioral Finance

T. Hens and M. O. Rieger · Quantitative Finance, 12, no. 10, 1487–1489

1995

Dynamics: An Introduction

In Mind as Motion: Explorations in the Dynamics of Cognition, R. F. Port and T. Van Gelder, eds., MIT Press, 45–68

1992

Book Review: Measure, Topology, and Fractal Geometry by G. A. Edgar

American Mathematical Monthly, 99, no. 4, 378–382

Mentorship

PhD Students

Student	Year	Dissertation Topic	Placement
Navid Bahadoran	current	Random matrix theory	—
Farez Siddiqui	current	State-dependent limit order book modeling	—
Ololade Sowunmi	2026	High-dimensional minimum variance optimization	Wells Fargo, NC
Hubeyb Gurdogan	2021	Eigenvector shrinkage for estimating covariance matrices	Postdoctoral Scholar, UC Berkeley
Heting Yan	2020	Machine learning and the limit order book	Microsoft
Navid Salehy	2019	Random walks over point processes and applications in finance	Dept. of Mathematics, University of New Orleans
Chenchen Zhou	2017	Multidimensional default threshold model for credit risk	Wells Fargo, NC
Yuanda Chen	2017	Modeling the limit order book using Hawkes processes	Goldman Sachs, NY
Chun-Yuan Chiu	2016	Modeling credit risk in the default threshold framework	Bank of America Merrill Lynch, NY
Dawna Jones	2015	Asset pricing equilibria for heterogeneous, limited-information agents (co-dir. P. Beaumont)	Wells Fargo, Charlotte, NC
Pierre Garreau	2013	Jump dependence and multidimensional default risk	Deutsche Bank, Jacksonville, FL
Yuan Zhang	2013	Modeling high-frequency order book dynamics with support vector machines	Yahoo!, Sunnyvale, CA
Henry Huang	2012	Modeling order book processes using queues and point processes	Quant, AllianceBernstein, NYC
Yang Liu	2012	Risk forecasting and portfolio optimization with GARCH, skewed t distributions	Quant, Florida State Board of Administration
Tianyu Liang	2012	Alternative models for stochastic volatility corrections (co-dir. X. Wang)	Quantitative Derivatives Analyst, ING, Philadelphia
Michelle Guan	2011	Asset market dynamics of heterogeneous agent models with learning (co-dir. P. Beaumont)	Asst. Professor, Indiana University Northwest
Juan Moreno	2007	Impulse control problems under non-constant volatility	Quant, Investment Board of Wisconsin
Andrew Culham	2007	Asset pricing with boundedly rational, heterogeneous agents (co-dir. P. Beaumont)	Quantitative Analyst, Florida Power and Light
Jianke Zhang	2007	Numerical methods for portfolio risk estimation	Quantitative Analyst, Florida Power and Light
Wenbo Hu	2005	Calibration of multivariate generalized hyperbolic distributions with the EM algorithm	Quant, Bell Trading, Chicago
Brian Tandy	1997	Cantor sets and Lipschitz actions on circles and trees (UT Austin)	Digeo Corp., Palo Alto
Paul Fabel	1994	Self-homeomorphisms of the 2-sphere (UT Austin)	Asst. Professor, Mississippi State University

Education

Teaching

I teach a variety of undergraduate and graduate mathematics courses. Recently taught FSU courses include MGF 3301 Intro to Advanced Math, MAA 4402 Complex Variables, MAC 2312 Calculus II, MAS 3105 Linear Algebra, MAA 4226 Advanced Calculus, MAP 6621 Financial Engineering I, MAA 5616 Measure and Integration. Detailed course information, syllabi, and materials for enrolled students are available through Canvas (FSU login required).

Events

Seminars & Conferences

📅 Financial Mathematics Seminar (weekly) 🏛 Mathematics in Industry Symposium (annual)

Get in touch

Contact

Email

Contact via FSU directory

Mailing Address

Department of Mathematics
Florida State University
1017 Academic Way, Room 208
Tallahassee, FL 32306-4510 USA