Research

Research Interests

• Mathematical finance: stochastic portfolio theory, arbitrage theory, roughness in finance.

• Stochastic analysis: pathwise development of Itô calculus and stochastic processes, applications to PDE, and mean-field interacting particle systems.

Publications and Preprints

• On isomorphism of the space of α-Hölder continuous functions with finite p-th variation, with P. Das.

Preprint, 2024.

• Hölder regularity and roughness: Construction and examples, with E. Bayraktar and P. Das.

Bernoulli, 2025, Volume 31, Issue 2, 1084-1113.

• Concentration of measure for graphon particle system, with E. Bayraktar.

Advances in Applied Probability, 2024, Volume 56, Issue 4, 1279-1306.

• A trajectorial approach to entropy dissipation for degenerate parabolic equations, with L. C. Yeung.

Bernoulli, 2024, Volume 30, Issue 3, 2253-2274.

• Quantifying dimensional change in stochastic portfolio theory, with E. Bayraktar and A. Tilva.

Mathematical Finance, 2024, Volume 34, Issue 3, 977-1021.

• Arbitrage theory in a market of stochastic dimension, with E. Bayraktar and A. Tilva.

Mathematical Finance, 2024, Volume 34, Issue 3, 847-895.

• Market-to-book ratio in stochastic portfolio theory.

Finance and Stochastics, 2023, Volume 27, Issue 2, 401-434.

• Local times for continuous paths of arbitrary regularity. 

Journal of Theoretical Probability, 2022, Volume 35, Issue 4, 2540-2568.

• Open markets, with I. Karatzas.

Mathematical Finance, 2021, Volume 31, Issue 4, 1111-1161.

• Trading strategies generated pathwise by functions of market weights, with I. Karatzas.

Finance and Stochastics, 2020, Volume 24, Issue 2, 423-463.