MMath Mathematics @ University of Manchester
Solved the nonlinear LWR conservation law with a conservative Godunov demand–supply scheme across grids of 1 to 36 junctions, paired with a 96-state shared Q-learning controller that raises junction flux by up to 2.9% and cuts total time spent by 7–19%.
Python, NumPy, FastAPI, PDEs
Derived the Black–Scholes PDE and Greeks from a delta-hedging argument via Itô's Lemma, validated the call price against $10^6$-path Monte Carlo ($10.45$ vs. $10.47 \pm 0.01$), and simulated discrete delta hedging over $20{,}000$ paths (log–log slope $-0.49$).
Python, NumPy, SciPy