Trading with the STARS: Algorithm Design & Spectrum of Fundamental Limits for Trading with Storage

2026-10-05

AI Summary

This study addresses online trading under storage constraints, aiming to optimize buying and selling decisions given a known price distribution in order to minimize regret. Drawing upon online learning theory, the proposed approach approximates the value function through repeated simulations across multiple scenarios, revealing how the median gap and initial inventory influence policy performance. The work establishes a novel hierarchy of fundamental limits and introduces the STARS algorithm, which achieves near-optimal performance. Specifically, it derives an O(log T) regret bound for finite atomic price distributions and a problem-dependent polynomial regret bound for continuous price distributions.

Abstract

We study an online trading problem where a trader, given a sequence of i.i.d. prices drawn from a known distribution $F$ on $[0,1]$, must make irrevocable buy, sell, or hold decisions subject to storage constraints. We investigate achievable algorithmic performance measured in terms of regret, the difference between the expected profit of the hindsight optimal policy that knows the entire price sequence and an online algorithm. We analyze finite atomic and continuous distributions characterized by their local behavior around the median which we capture using a parameter $β$. The parameter $β$ quantifies how the mass of prices accumulates around the distribution median. We identify a new driver of algorithmic performance, demonstrating that median gaps coupled with an initial inventory level of zero can force regret scaling of $Ω(T^{(β+ 1)/(2β+4)})$ --- establishing a novel spectrum of fundamental limits on algorithmic performance. We then study STARS, short for Storage Trading by Averaging Repeatedly across multiple Scenarios, which simulates possible future price scenarios to approximate the value-to-go function and make buy/sell/hold decisions. We show that STARS obtain near-optimal algorithmic performance (upto poly-logarithmic factors) across a broad range of distributions. In particular, it achieves $O(\log T)$ regret for finite atomic prices, $\widetilde{O}(T^{β/(2β+2)})$ for continuous distributions without a median gap and $\widetilde{O}(T^{(β+1)/(2β+4)})$ for continuous distributions with a median gap for $β\geq 0$.

Problem

• online trading
• storage constraints
• regret minimization
• fundamental limits
• price distribution

Innovation

• Online trading
• Regret analysis
• STARS algorithm
• Fundamental limits
• Value-to-go approximation