Yang Azzollini
DPhil, University of Oxford · yang.maths@gmail.com · GitHub
I work on statistical methods for multivariate processes observed on asynchronous grids — the kind of problem that shows up in autonomous driving, production ML telemetry, medical monitoring, and high-frequency finance. Concretely: two univariate processes, each observed on its own irregular timestamp grid, and the task is to estimate their covariance.
In my DPhil thesis I worked out the exact finite-sample variance for a family of covariance estimators on asynchronous data. Peter Clifford and Brian Ripley supervised the work. In 2026 I proved that the class is optimal in a strong sense, and formalised the proofs in Lean 4 with Mathlib.
Research
2026 paper (in preparation)
Optimal weighted Zhou–Hayashi–Yoshida estimators for asynchronous covariance. Extends the 2016 thesis to the full-variance optimality problem for general ρ², with a two-step plug-in construction and a Cramér–Rao efficiency statement at ρ=0. Target venue: Journal of Financial Econometrics.
Lean 4 formalisation
Five Lean modules, zero sorrys. The thesis’s Theorem 5.1 (exact variance of the extended-ZHY class) and the 2026 Theorems 2–4 are machine-verified.
2016 DPhil thesis
Correlation methods in the statistical analysis of financial trading data. University of Oxford. The thesis established the exact finite-sample variance of the extended Zhou–Hayashi–Yoshida estimator class, completing a finite-sample result that the asymptotic literature had left open.
Education
BA in Mathematics and Computer Science, St Hugh's College, University of Oxford.
MSc in Applied Statistics, St Hugh's College, University of Oxford. Supervisor: Brian Ripley.
DPhil in Statistics, Lady Margaret Hall, University of Oxford. Supervisors: Peter Clifford and Brian Ripley.
Background
I stumbled upon these problems on a trading desk at a top investment bank, which also sponsored my research. Volatility, asynchronous correlation, and lead-lag looked like three different questions at the time; they turned out to share the same mathematical structure, and that structure has been worth decades of work. I currently live in Silicon Valley, still working on problems that no one really understands yet.