Publications

Research papers in quantitative finance and quantum machine learning.

Online Estimation and Optimization of Utility-Based Shortfall Risk

Menon, Arvind S., Prashanth L. A., and Jagannathan, Krishna

Mathematics of Operations Research, INFORMS — 2023 · 48(4), 2444–2470

Utility-Based Shortfall Risk (UBSR) is a risk metric increasingly popular in financial applications due to properties it enjoys over classical VaR/CVaR measures. We consider estimating UBSR in a recursive online setting, casting the problem as root-finding and proposing stochastic approximation schemes. We derive non-asymptotic bounds on estimation error and extend to UBSR optimization over a parameterized class of random variables using stochastic gradient descent, with convergence guarantees.

Published version arXiv preprint

Q-means using Variational Quantum Feature Embedding

Menon, Arvind S., and Puri, Nikaash

arXiv Preprint — 2021

A hybrid quantum-classical algorithm that learns a quantum feature map to separate non-linearly separable data in the classical space. A variational quantum circuit embeds classical data into a Hilbert space where q-means clustering is applied. The circuit is optimized by minimizing Hilbert-Schmidt distance between characteristic cluster quantum states, using gradient of the expectation value to update variational parameters.

arXiv preprint