arXiv subjects

Xiaofei Shi

Publications and source records attributed to Xiaofei Shi.

23 records · Page 2Linked to original sources

arXiv2020

An Equilibrium Model for the Cross-Section of Liquidity Premia

We study a risk-sharing economy where an arbitrary number of heterogenous agents trades an arbitrary number of risky assets subject to quadratic transaction costs. For linear state dynamics, the forward-backward stochastic differential equations characterizing equilibrium asset prices and trading strategies in this context reduce to a system of matrix-valued Riccati equations. We prove the existence of a unique global solution and provide explicit asymptotic expansions that allow us to approximate the corresponding equilibrium for small transaction costs. These tractable approximation formulas make it feasible to calibrate the model to time series of prices and trading volume, and to study the cross-section of liquidity premia earned by assets with higher and lower trading costs. This is illustrated by an empirical case study.

q-fin.GN↗

arXiv2020

Asset Pricing with General Transaction Costs: Theory and Numerics

We study risk-sharing equilibria with general convex costs on the agents' trading rates. For an infinite-horizon model with linear state dynamics and exogenous volatilities, we prove that the equilibrium returns mean-revert around their frictionless counterparts - the deviation has Ornstein-Uhlenbeck dynamics for quadratic costs whereas it follows a doubly-reflected Brownian motion if costs are proportional. More general models with arbitrary state dynamics and endogenous volatilities lead to multidimensional systems of nonlinear, fully-coupled forward-backward SDEs. These fall outside the scope of known wellposedness results, but can be solved numerically using the simulation-based deep-learning approach of Han, Jentzen and E (2018). In a calibration to time series of prices and trading volume, realistic liquidity premia are accompanied by a moderate increase in volatility. The effects of different cost specifications are rather similar, justifying the use of quadratic costs as a proxy for other less tractable specifications.

q-fin.MF↗

arXiv2020

On Strategyproof Conference Peer Review

We consider peer review in a conference setting where there is typically an overlap between the set of reviewers and the set of authors. This overlap can incentivize strategic reviews to influence the final ranking of one's own papers. In this work, we address this problem through the lens of social choice, and present a theoretical framework for strategyproof and efficient peer review. We first present and analyze an algorithm for reviewer-assignment and aggregation that guarantees strategyproofness and a natural efficiency property called unanimity, when the authorship graph satisfies a simple property. Our algorithm is based on the so-called partitioning method, and can be thought as a generalization of this method to conference peer review settings. We then empirically show that the requisite property on the authorship graph is indeed satisfied in the submission data from the ICLR conference, and further demonstrate a simple trick to make the partitioning method more practically appealing for conference peer review. Finally, we complement our positive results with negative theoretical results where we prove that under various ways of strengthening the requirements, it is impossible for any algorithm to be strategyproof and efficient.

cs.GT↗

arXiv2019

Sublinear Time Numerical Linear Algebra for Structured Matrices

We show how to solve a number of problems in numerical linear algebra, such as least squares regression, $\ell_p$-regression for any $p \geq 1$, low rank approximation, and kernel regression, in time $T(A) \poly(\log(nd))$, where for a given input matrix $A \in \mathbb{R}^{n \times d}$, $T(A)$ is the time needed to compute $A\cdot y$ for an arbitrary vector $y \in \mathbb{R}^d$. Since $T(A) \leq O(\nnz(A))$, where $\nnz(A)$ denotes the number of non-zero entries of $A$, the time is no worse, up to polylogarithmic factors, as all of the recent advances for such problems that run in input-sparsity time. However, for many applications, $T(A)$ can be much smaller than $\nnz(A)$, yielding significantly sublinear time algorithms. For example, in the overconstrained $(1+ε)$-approximate polynomial interpolation problem, $A$ is a Vandermonde matrix and $T(A) = O(n \log n)$; in this case our running time is $n \cdot \poly(\log n) + \poly(d/ε)$ and we recover the results of \cite{avron2013sketching} as a special case. For overconstrained autoregression, which is a common problem arising in dynamical systems, $T(A) = O(n \log n)$, and we immediately obtain $n \cdot \poly(\log n) + \poly(d/ε)$ time. For kernel autoregression, we significantly improve the running time of prior algorithms for general kernels. For the important case of autoregression with the polynomial kernel and arbitrary target vector $b\in\mathbb{R}^n$, we obtain even faster algorithms. Our algorithms show that, perhaps surprisingly, most of these optimization problems do not require much more time than that of a polylogarithmic number of matrix-vector multiplications.

cs.LG↗

arXiv2018

Improved Algorithms for Adaptive Compressed Sensing

In the problem of adaptive compressed sensing, one wants to estimate an approximately $k$-sparse vector $x\in\mathbb{R}^n$ from $m$ linear measurements $A_1 x, A_2 x,\ldots, A_m x$, where $A_i$ can be chosen based on the outcomes $A_1 x,\ldots, A_{i-1} x$ of previous measurements. The goal is to output a vector $\hat{x}$ for which $$\|x-\hat{x}\|_p \le C \cdot \min_{k\text{-sparse } x'} \|x-x'\|_q\,$$ with probability at least $2/3$, where $C > 0$ is an approximation factor. Indyk, Price and Woodruff (FOCS'11) gave an algorithm for $p=q=2$ for $C = 1+ε$ with $\Oh((k/ε) \loglog (n/k))$ measurements and $\Oh(\log^*(k) \loglog (n))$ rounds of adaptivity. We first improve their bounds, obtaining a scheme with $\Oh(k \cdot \loglog (n/k) +(k/ε) \cdot \loglog(1/ε))$ measurements and $\Oh(\log^*(k) \loglog (n))$ rounds, as well as a scheme with $\Oh((k/ε) \cdot \loglog (n\log (n/k)))$ measurements and an optimal $\Oh(\loglog (n))$ rounds. We then provide novel adaptive compressed sensing schemes with improved bounds for $(p,p)$ for every $0 < p < 2$. We show that the improvement from $O(k \log(n/k))$ measurements to $O(k \log \log (n/k))$ measurements in the adaptive setting can persist with a better $ε$-dependence for other values of $p$ and $q$. For example, when $(p,q) = (1,1)$, we obtain $O(\frac{k}{\sqrtε} \cdot \log \log n \log^3 (\frac{1}ε))$ measurements.

cs.DS↗