I'm a graduate student in Applied Mathematics and Statistics at Stony Brook University, concentrating in quantitative finance. I like to analyze a model mathematically before I build it: whether its structure fits the problem, whether its likelihood or loss targets the right quantity, and what goes wrong when either is misspecified. That analysis shapes which model I choose, how I implement it and how I test it.
My background in software engineering helps me put these ideas into practice, from implementing models and numerical solvers to building research pipelines and trading systems. I've applied this combination through equity alpha research at SMB Capital and independent quantitative development work.
- Sequential decision-making and online learning: stochastic control, reinforcement learning and adaptive control, with a focus on exploration and learning dynamics: how fast methods converge on real problems and what bounds they come with.
- Statistical modeling and inference: how the estimation target and assumptions about the data-generating process guide the choice of models and estimators. I'm interested in robustness to model misspecification and finite-sample performance, especially for nonparametric and high-dimensional methods: kernel methods, low-rank estimation and random matrix theory.
- Applications in quantitative finance: alpha discovery, dynamic portfolio construction, derivatives pricing, and optimal quoting in market making.
I'm currently exploring neural PDE methods for stochastic control and computational methods for inference.
How does a crowd of investors invest when each one fears ending the year below the average?
Each investor chooses how much to put in a risky asset and is penalised for ending below the population's average wealth. That average is itself the result of everyone's choices, so the problem is a mean-field game: an HJB equation for each investor's best strategy, a Fokker–Planck equation for how the population's wealth evolves, and a fixed point where the average investors plan against is the average they produce. It has the same structure as heterogeneous-agent macro models (Aiyagari; Achdou, Han, Lasry, Lions & Moll), with peer comparison in place of an interest rate.
What we did
- Found that the problem as originally posed let peers have no effect on anyone's choices, and redesigned the penalty so individual strategies and the crowd shape each other.
- Built finite-difference solvers for both equations and the equilibrium search as the benchmark, with errors of about 10⁻⁶ (checked against the exact no-penalty solution and by grid refinement).
- Solved the same system with physics-informed neural networks (PyTorch), matching the benchmark equilibrium to 0.014%.
- Extended the model to an N-player Nash equilibrium, solving PDEs in up to 21 variables with PINNs, where grid methods are infeasible.
What it shows
- Fear of falling behind halves the average amount invested in the risky asset, and wealth piles up just below the average.
- The population's average one-year return falls from 11.0% to 6.5%: competing on relative performance costs everyone return.
- The result barely depends on what investors expect: any belief about the average between 1.0 and 1.3 leads to a realised average between 1.059 and 1.070.
Python · PyTorch · NumPy/SciPy · finite differences · PINNs · AMS 516, Stony Brook · joint work with Ander Ibarrondo
When the quantity you need is a 1% tail quantile, should you model it directly, or model the whole return distribution and read the quantile off?
On a crypto perpetual future with isolated margin, a position at leverage L is liquidated when its
worst adverse move over the holding window reaches 1/L − mmr (mmr: maintenance margin rate). Keeping
the chance of liquidation at α means forecasting the α-quantile of that move and setting
L = 1/(mmr + |q̂_α|). Leverage is a direct readout of the forecast: overstate the tail and you give
up leverage; understate it and positions are liquidated more often than promised.
What we did
- Compared six estimators of the conditional tail quantile: distributional models (OLS with normal errors, GARCH(1,1)-t), direct quantile models (historical quantile, linear and kernel-weighted quantile regression) and a conservative CVaR regression.
- Fitted quantile regression pooled across coins with coin fixed effects on four market-state factors (funding, open-interest change, realized volatility, basis), using PSG.
- Evaluated out of sample on 7 Binance perpetuals (about 36,000 8-hour windows, 2022–2026) with 51 monthly walk-forward refits, testing liquidation rates for correct coverage (Kupiec) and independence (Christoffersen).
What it shows
- Modelling the quantile directly wins. Pooled quantile regression liquidated 1.00% of long positions at a 1% target, with all 7 coins within Kupiec bounds, at 13% more leverage than the historical-quantile rule (14.5× vs 12.8×).
- Distributional models pay for misspecified tails. Normal tails are too thin: OLS liquidates 2.6–3.3% at a 1% target. GARCH-t's extra leverage for longs comes with extra liquidations (1.38%).
- More flexibility did not help. The nonparametric kernel model did not beat linear quantile regression.
- CVaR regression is conservative by design: well below target, with a quarter to a third less leverage than quantile regression.
- Limitations: at 1% short, every method except CVaR liquidates too often (GARCH-t comes closest, at 1.12%); liquidations cluster in time; fees and funding are excluded.
Full results: liquidation rate / average leverage, out of sample
| Method | 1% long | 1% short | 5% long | 5% short |
|---|---|---|---|---|
| Historical quantile | 1.23% / 12.8× | 1.27% / 12.9× | 5.01% / 20.7× | 5.16% / 21.2× |
| OLS, normal errors | 2.60% / 17.8× | 3.30% / 18.9× | 4.81% / 22.1× | 5.75% / 23.4× |
| GARCH(1,1)-t | 1.38% / 15.3× | 1.12% / 14.5× | 6.11% / 24.8× | 5.75% / 24.1× |
| Quantile regression | 1.00% / 14.5× | 1.35% / 15.3× | 4.76% / 23.6× | 5.31% / 23.9× |
| Kernel-weighted quantile | 1.14% / 13.7× | 1.35% / 14.1× | 5.08% / 22.9× | 5.59% / 23.2× |
| CVaR regression | 0.41% / 10.6× | 0.48% / 11.6× | 1.43% / 16.1× | 1.83% / 17.0× |
Python · statsmodels · PSG · quantile regression · GARCH · CVaR · AMS 518, Stony Brook · joint work with Marcus Minutello