arXiv subjects

Kyle Sung

Publications and source records attributed to Kyle Sung.

3 recordsLinked to original sources

arXiv2026

Sharpe Ratio and Return-VaR Ratio Maximization for Option Portfolios with Skew-Elliptical $t$ Underlying Returns

We provide a formulation for optimal option portfolios under Sharpe Ratio maximization when the underlying returns follow a skew-elliptical t-distribution. This departs from the traditional normal returns setting in the context of Sharpe ratio maximization by allowing the modelling of heavy-tailed and skewed dynamics. The novelty of this paper and our main result is to provide explicit formulas for the portfolio weights when maximizing the Sharpe ratio and return-to-Value-at-Risk (VaR) ratio in the skew-elliptical setting. Numerical experiments reveal that the optimal portfolios for the two ratios are different.

q-fin.PM↗

arXiv2026

Optimal Option Portfolios for Skew-Elliptical t Returns

This paper explores option portfolio optimization when the underlying returns are skew-elliptical t-distributed. We use the variance and value at risk (VaR) to measure portfolio risk. The novelty of our work is the departure from the traditional normal returns setting, allowing investors to capture both heavy-tailed and skewed market dynamics. We provide explicit portfolio weights for the variance and VaR approximation. Our second contribution is the numerical representation of portfolio weights, obtained from numerical optimization for better VaR approximations. The effect of skewness on the portfolio weights is quantified by comparing our optimal skew t weights with those generated in the Student t setting. We also find that, as expected, a better VaR approximation risk measure yields optimal portfolio weights which are more different than the variance optimal weights.

q-fin.PM↗

arXiv2025

Step by Step: Adaptive Gradient Descent for Training L-Lipschitz Neural Networks

We demonstrate that applying an eventual decay to the learning rate (LR) in empirical risk minimization (ERM), where the mean-squared-error loss is minimized using standard gradient descent (GD) for training a two-layer neural network with Lipschitz activation functions, ensures that the resulting network exhibits a high degree of Lipschitz regularity, that is, a small Lipschitz constant. Moreover, we show that this decay does not hinder the convergence rate of the empirical risk, now measured with the Huber loss, toward a critical point of the non-convex empirical risk. From these findings, we derive generalization bounds for two-layer neural networks trained with GD and a decaying LR with a sub-linear dependence on its number of trainable parameters, suggesting that the statistical behaviour of these networks is independent of overparameterization. We validate our theoretical results with a series of toy numerical experiments, where surprisingly, we observe that networks trained with constant step size GD exhibit similar learning and regularity properties to those trained with a decaying LR. This suggests that neural networks trained with standard GD may already be highly regular learners.

stat.ML↗