Schrödinger bridges for tail-risk scenarios
SPY return paths under stochastic volatility and jumps.
7
generative models benchmarked
3–13×
baseline error on jumps
5,068
daily windows
École Polytechnique
Applied Math
Ingénieur · 2025–27
MathsFI Lab
Generative models
with Prof. Huyên Pham
IMC Prosperity
Top 1.5%
280 / 18,803 teams
QRT Data Challenge
#1
public leaderboard
01 / Lab
See, don't read.
click: toxic flow · drag: rotate
Order book under toxic flow
\[\delta_t=\gamma\sigma_t^2+\tfrac{2}{\gamma}\ln\!\big(1+\tfrac{\gamma}{k}\big)+\alpha\,\pi_t\]
spread (ticks)
—
toxicity \(\pi_t\)
—
\(\sigma_t\)
—
mid move (ticks)
—
drag: rotate · envelope: ±2σ price risk of unexecuted shares (×3)
Almgren–Chriss execution
\[x^\star(t)=X\,\frac{\sinh\kappa(T-t)}{\sinh\kappa T},\quad \kappa^2\simeq\frac{\lambda\sigma^2}{\eta}\]
\(\mathbb{E}[\mathrm{IS}]\)
—
\(\mathrm{SD}[\mathrm{IS}]\)
—
\(\kappa\)
—
inventory half-life
—
efficient frontier · \(\mathbb{E}[\mathrm{IS}]\) vs \(\mathrm{SD}[\mathrm{IS}]\)
drag: rotate · hover: smile
σ 5% → 65%
SSVI volatility surface
\[w=\tfrac{\theta_T}{2}\Big(1+\rho\varphi k+\sqrt{(\varphi k+\rho)^2+1-\rho^2}\Big)\]
ATM 1M
—
ATM 2Y
—
1Y skew \(\partial\sigma/\partial k\)
—
3M 80% put − ATM
—
pathsfitted uₙexact
Deep backward scheme · 100-d HJB
\[Y_n=\mathbb{E}\big[\,Y_{n+1}-\lambda\lVert\nabla u_{n+1}\rVert^2\Delta t\;\big|\;X_n\big]\]
scheme \(Y_0\)
—
exact \(u(0,0)\)
—
rel. error
—
runtime
—
noise → data
particlestarget
Schrödinger bridge
\[X_t=(1-t)\,x_0+t\,x_1+\sqrt{\varepsilon}\,(W_t-tW_1)\]
Sinkhorn iters
—
\(\lVert\pi\mathbf{1}-a\rVert_1\)
—
\(\mathbb{E}\lVert X_1-X_0\rVert^2\)
—
\(\varepsilon\)
—
IPF convergence · \(\log_{10}\) marginal error
highlighted marketnoise flow
Kyle–Back equilibrium
\[dP_t=\lambda\,(dX_t+dZ_t),\quad \lambda=\frac{\sigma_v}{\sigma_u}\]
impact \(\lambda\)
—
\(\mathbb{E}[\pi]=\sigma_v\sigma_u\)
—
price vol
—
info by \(t=\tfrac12\)
—
02 / Work
Selected work
Cross-sectional alpha, CSI 300
Nonlinear temporal features, point-in-time OOS, net of costs.
.031→.038
rank IC
.78→.91
net IR
Probabilistic traffic forecasting
Forecasts tied to SLA cost; root-cause search on a network digital twin.
1.68→0.48
MASE
4.43→1.28
CRPS
13.8→1.6%
delay error
Competitions
Algorithmic trading, allocation forecasting, mathematical modelling.
Top 1.5%
IMC Prosperity
#1
QRT public LB
0.17%
CSIAM national 2nd prize
Queue-reactive order book simulator
Huang–Lehalle–Rosenbaum: queue-size-dependent limit, cancel and market order intensities.
HLR
queue-reactive model
Surrogates for inverse problems
SVD-autoencoder latent state, kNN surrogate, coarse-to-fine search.
<0.1 s
per inference
~0.3%
L2 error
3
journal papers
03 / Principles
Four equations
\[p(\theta \mid \mathcal{D}) \propto p(\mathcal{D} \mid \theta)\, p(\theta)\]
Uncertainty first
\[\hat{\Sigma} = \delta F + (1-\delta)\, S\]
Shrink before optimising
\[\mathrm{IR}_{\text{net}} = \frac{\mathbb{E}[\,r - c\,]}{\sigma(r - c)}\]
Net of costs
\[dX_t = b\,dt + \sigma\,dW_t + dJ_t\]
Derive, then fit
04 / Publications
Peer-reviewed
- 2025Decision tree based parameter identification and state estimation: application to Reactor Operation Digital TwinHong, L. et al. · Nuclear Engineering and Technology
- 2024Optimizing near-carbon-free nuclear energy systems: advances in reactor operation digital twin through hybrid machine learning algorithmsHong, L. et al. (first author) · Nuclear Science and Techniques
- 2024A noise and vibration tolerant ResNet for field reconstruction with sparse sensorsHong, L. et al. · Communications in Computational Physics
05 / Stack
Toolkit
codePythonPyTorchNumPyPandasscikit-learnSQLJavaMATLABGitLinux
mathSDEsStochastic calculusMonte CarloRare eventsOptimal transportBayesian inferenceNumerical optimisation
mlGenerative modelsDeep learningTime-series forecastingLLM agents
quantAlpha researchFactor modelsBacktestingOOS validationMicrostructurePortfolio optimisationCovariance estimation
lang中文EnglishFrançais
06 / About
Desk and iron.
SJTU computer science → École Polytechnique applied mathematics. Head of Quant at X-Finance.
2023 Shanghai intercollegiate bodybuilding champion. Rugby, American football, Hyrox.
Writing →