Xuran Lyu

I am a Master’s student in Economics at Duke University. My academic work sits at the intersection of mathematical finance, stochastic analysis, time series, and functional analysis.

Before Duke, I completed a B.S. at the University of Miami with triple majors in Mathematics (Computational), Economics (Political), and Philosophy. That background still shapes the way I work: I like problems where technical structure, modeling choices, and conceptual interpretation have to be held together.

My current focus is rough volatility: numerical methods for the rough Heston model via the fractional Riccati equation, asymptotic regimes in option pricing, and statistical inference for rough volatility using high-frequency option data. I am also interested in the computational side of quantitative finance, including high-frequency trading systems and C++ implementation.

The broader structure behind these interests is functional analysis. I am drawn to places where the same mathematical language reappears across finance, physics, time series, and PDEs: Hilbert spaces, operators, Fourier transforms, Green’s functions, characteristic functions, and integral equations.

Alongside the technical work, I keep a parallel set of interests in philosophy of mathematics, metaphysics, political philosophy, Chinese intellectual history, world history, film, and the beauty of mathematical structures. I have not opened a public writing section yet; I want that page to appear only when there are finished essays worth reading rather than placeholders.