Andrew Papanicolaou
· Associate Professor, MathematicsNorth Carolina State University · Finance
Active 1977–2025
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About
Andrew Papanicolaou is an Associate Professor in the Department of Mathematics at North Carolina State University. His research interests include probability theory, nonlinear filtering, stochastic control, and financial mathematics. In Fall 2023, the NCSU Department of Mathematics hosted the 7th Eastern Conference in Mathematical Finance, reflecting the department's active engagement in the field.
Research topics
- Artificial Intelligence
- Neuroscience
- Psychology
- Computer Science
- Medicine
- Radiology
- Physics
Selected publications
State Constrained Stochastic Optimal Control Using LSTMs
2021-05-25 · 12 citations
articleIn this paper, we propose a new methodology for state constrained stochastic optimal control (SOC) problems. The solution is based on past work in solving SOC problems using forward-backward stochastic differential equations (FB-SDE). Our approach in solving the FBSDE utilizes a deep neural network (DNN), specifically Long Short-Term Memory (LSTM) networks. LSTMs are chosen to solve the FBSDE to address the curse of dimensionality, non-linearities, and long time horizons. In addition, the state…
Automatica · 2023-06-26 · 8 citations
articlePrincipal Eigenportfolios for U.S. Equities
SIAM Journal on Financial Mathematics · 2022-07-18 · 6 citations
articleWe analyze portfolios constructed from the principal eigenvector of the equity returns' correlation matrix and compare these portfolios with the capitalization weighted market portfolio. It is well known empirically that principal eigenportfolios are a good proxy for the market portfolio. We quantify this property through the large-dimensional asymptotic analysis of a spike model with diverging top eigenvalue, comprising a rank-one matrix and a random matrix. We show that, in this limit, the top…
IEEE Access · 2023-01-01 · 4 citations
articleOpen access1st authorCorrespondingWe analyze a fixed-point algorithm for reinforcement learning (RL) of optimal portfolio mean-variance preferences in the setting of multivariate generalized autoregressive conditional-heteroskedasticity (MGARCH) with a small penalty on trading. A numerical solution is obtained using a neural network (NN) architecture within a recursive RL loop. A fixed-point theorem proves that NN approximation error has a big-oh bound that we can reduce by increasing the number of NN parameters. The functional…
The Journal of Computational Finance · 2023-01-01 · 4 citations
article1st authorCorrespondingWe simulate the execution of a large stock order with real data and a general power law in the Almgren and Chriss model. The example we consider is the liquidation of a large position executed over the course of a single trading day in a limit order book. Transaction costs are incurred because large orders walk the order book (that is, they consume order book liquidity beyond the best bid/ask price). We model the order book with a power law that is proportional to trading volume, and thus transa…
Recent grants
NIH · $2.5M · 2004
Texas Center for Learning Disabilities
NIH · $53.5M · 2006–2023
Deep Neural Networks for Solving Non-Markov Optimization Problems
NSF · $174k · 2019–2021
Frequent coauthors
- 151 shared
Panagiotis G. Simos
University of Crete
- 101 shared
Roozbeh Rezaie
Le Bonheur Children's Hospital
- 95 shared
James W. Wheless
- 83 shared
Joshua I. Breier
Texas Medical Center
- 63 shared
George Zouridakis
University of Houston
- 60 shared
Shalini Narayana
- 55 shared
Eduardo M. Castillo
AdventHealth for Children
- 54 shared
Jack Μ. Fletcher
University of Houston
Labs
Education
- 1990
Ph.D., Mathematics
University of California, Berkeley
- 1985
M.S., Mathematics
University of California, Berkeley
- 1983
B.S., Mathematics
University of California, Berkeley
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