publications

Working papers, in preparation, and forthcoming work.

Notes

Summer Mathematics Learning Notes. Open-access learning notes on real analysis, topology, measure theory, functional analysis, elliptic PDE, complex analysis, and philosophy of mathematics. PDF

2026

Numerical Methods for the Rough Heston Model via the Fractional Riccati Equation

Xuran Lyu

2026

Working paper, in preparation

Abs

We propose a high-order Adams scheme for the fractional Riccati equation arising in the calibration of the rough Heston volatility model. Asymptotic analysis is carried out for both short- and long-maturity regimes, and numerical experiments demonstrate convergence rates and stability properties.
Economics Research Project

Xuran Lyu and collaborators

2026

In preparation

Abs

Abstract to be added once the project crystallizes.
Statistical Inference for Rough Volatility Using High-Frequency Option Data

Xuran Lyu and collaborators

2026

In preparation

Abs

Abstract to be added once the project crystallizes.
Probability Project

Xuran Lyu

2026

In preparation

Abs

Abstract to be added.