arXiv subjects

Victor Xu

Publications and source records attributed to Victor Xu.

3 recordsLinked to original sources

arXiv2026

Autodeleveraging as Online Learning

Autodeleveraging (ADL) is a last-resort loss socialization mechanism used by perpetual futures venues when liquidation and insurance buffers are insufficient to restore solvency. Despite the scale of perpetual futures markets, ADL has received limited formal treatment as a sequential control problem. This paper provides a concise formalization of ADL as online learning on a PNL-haircut domain: at each round, the venue selects a solvency budget and a set of profitable trader accounts. The profitable accounts are liquidated to cover shortfalls up to the solvency budget, with the aim of recovering exchange-wide solvency. In this model, ADL haircuts apply to positive PNL (unrealized gains), not to posted collateral principal. Using our online learning model, we provide robustness results and theoretical upper bounds on how poorly a mechanism can perform at recovering solvency. We apply our model to the October 10, 2025 Hyperliquid stress episode. The regret caused by Hyperliquid's production ADL queue is about 50\% of an upper bound on regret, calibrated to this event, while our optimized algorithm achieves about 2.6\% of the same bound. In dollar terms, the production ADL model over liquidates trader profits by up to \$51.7M. We also counterfactually evaluated algorithms inspired by our online learning framework that perform better and found that the best algorithm reduces overshoot to \$3M. Our results provide simple, implementable mechanisms for improving ADL in live perpetuals exchanges.

cs.GT↗

arXiv2021

Generalizing the Distribution of Missing Sums in Sumsets

Given a finite set of integers $A$, its sumset is $A+A:= \{a_i+a_j \mid a_i,a_j\in A\}$. We examine $|A+A|$ as a random variable, where $A\subset I_n = [0,n-1]$, the set of integers from 0 to $n-1$, so that each element of $I_n$ is in $A$ with a fixed probability $p \in (0,1)$. Recently, Martin and O'Bryant studied the case in which $p=1/2$ and found a closed form for $\mathbb{E}[|A+A|]$. Lazarev, Miller, and O'Bryant extended the result to find a numerical estimate for $\text{Var}(|A+A|)$ and bounds on the number of missing sums in $A+A$, $m_{n\,;\,p}(k) := \mathbb{P}(2n-1-|A+A|=k)$. Their primary tool was a graph-theoretic framework which we now generalize to provide a closed form for $\mathbb{E}[|A+A|]$ and $\text{Var}(|A+A|)$ for all $p\in (0,1)$ and establish good bounds for $\mathbb{E}[|A+A|]$ and $m_{n\,;\,p}(k)$. We continue to investigate $m_{n\,;\,p}(k)$ by studying $m_p(k) = \lim_{n\to\infty}m_{n\,;\,p}(k)$, proven to exist by Zhao. Lazarev, Miller, and O'Bryant proved that, for $p=1/2$, $m_{1/2}(6)>m_{1/2}(7) m_{p}(1)<m_{p}(2)$. Finally, we extend the graph-theoretic framework originally introduced by Lazarev, Miller, and O'Bryant to correlated sumsets $A+B$ where $B$ is correlated to $A$ by the probabilities $\mathbb{P}(i\in B \mid i\in A) = p_1$ and $\mathbb{P}(i\in B \mid i\not\in A) = p_2$. We provide some preliminary results using the extension of this framework.

math.NT↗

arXiv2018

When Sets Can and Cannot Have MSTD Subsets

A finite set of integers $A$ is a sum-dominant (also called an More Sums Than Differences or MSTD) set if $|A+A| > |A-A|$. While almost all subsets of $\{0, \dots, n\}$ are not sum-dominant, interestingly a small positive percentage are. We explore sufficient conditions on infinite sets of positive integers such that there are either no sum-dominant subsets, at most finitely many sum-dominant subsets, or infinitely many sum-dominant subsets. In particular, we prove no subset of the Fibonacci numbers is a sum-dominant set, establish conditions such that solutions to a recurrence relation have only finitely many sum-dominant subsets, and show there are infinitely many sum-dominant subsets of the primes.

math.NT↗