US-Equity options market-makingVolatility alpha research

Working with Professor Tarek Elgindi on mixing problems; related topics include Bressan's mixing conjecture and chaotic maps. Our current goals are to construct (and prove, of course) an exponentially-mixing vector field of Lipschitz regularity (currently the most regular examples are only a-Holder continuous for a < 1).https://arxiv.org/abs/2304.05374

Working with Professor Andrea Agazzi.Project 2: (also with Professor Jianfeng Lu)Investigating sample complexity of learning linear systems with memory. If the dynamics have n steps of memory, how does increasing the memory of our model affect sample complexity?Project 1:Developed new theoretical trick to prove convergence of policy gradient methods in the LQR setting for non-linear policies (which includes some simple neural network training regimes). https://arxiv.org/abs/2112.07612

Working with Professor Lillian Pierce to investigate a result about the number of lattice points on some arc of a circle. Working to improve the sharpness of the current bound on the number of lattice points in an arc of length R^theta. Wrote code in Rust (https://github.com/craigxchen/Jarnik) to calculate true values for large radii. Provided detailed, rigorous proofs to lemmas and theorems from "Trigonometric Polynomials and Lattice Points" by Cilleruelo and Cordoba that were not provided in the paper. Also provided detailed proof of a Lemma from Bourgain’s paper “On Strichartz’s Inequalities and the Nonlinear Schrödinger Equation on Irrational Tori”*Project paused from May 2020 to Oct 2020 due to COVID-19.

The only sophomore of 8 students selected to participate in a funded summer research fellowship. Continued my work with Prof. Agazzi and proved a stronger convergence result for policy gradient agents in the infinite-horizon, discounted LQR setting. Implemented RL agents using PyTorch to produce experimental results and verify intuition. For more information about the program: https://math.duke.edu/undergraduate/pruv

US-Equity options market-making

Torbett lab