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It is a common phenomenon that for high-dimensional and nonparametric statistical models, rate-optimal estimators balance squared bias and variance. Although this balancing is widely observed, little is known whether methods exist that…
We investigate the relative information efficiency of financial markets by measuring the entropy of the time series of high frequency data. Our tool to measure efficiency is the Shannon entropy, applied to 2-symbol and 3-symbol…
We present a set of log-price integrated variance estimators, equal to the sum of open-high-low-close bridge estimators of spot variances within $n$ subsequent time-step intervals. The main characteristics of some of the introduced…
We propose a microstructural modeling framework for studying optimal market making policies in a FIFO (first in first out) limit order book (LOB). In this context, the limit orders, market orders, and cancel orders arrivals in the LOB are…
We consider the models Y_{i,n}=\int_0^{i/n} \sigma(s)dW_s+\tau(i/n)\epsilon_{i,n}, and \tilde Y_{i,n}=\sigma(i/n)W_{i/n}+\tau(i/n)\epsilon_{i,n}, i=1,...,n, where W_t denotes a standard Brownian motion and \epsilon_{i,n} are centered i.i.d.…
With an ever-expanding ecosystem of noisy and intermediate-scale quantum devices, exploring their possible applications is a rapidly growing field of quantum information science. In this work, we demonstrate that variational quantum…
This research explores the development and application of the High-Order Dynamic Integration Method for solving integro-differential equations, with a specific focus on turbulent fluid dynamics. Traditional numerical methods, such as the…
Maximizing the computational utility of near-term quantum processors requires predictive noise models that inform robust, noise-aware compilation and error mitigation. Conventional models often fail to capture the complex error dynamics of…
This paper addresses the problem of learning linear dynamical systems from noisy observations. In this setting, existing algorithms either yield biased parameter estimates or have large sample complexities. We resolve these issues by…
We study the construction of a confidence interval (CI) for a simulation output performance measure that accounts for input uncertainty when the input models are estimated from finite data. In particular, we focus on performance measures…
We showcase how Quantile Regression (QR) can be applied to forecast financial returns using Limit Order Books (LOBs), the canonical data source of high-frequency financial time-series. We develop a deep learning architecture that…
In this paper, we first investigate the estimation of the empirical joint Laplace transform of volatilities of two semi-martingales within a fixed time interval [0, T] by using overlapped increments of high-frequency data. The proposed…
Assessment of practical quantum information processing (QIP) remains partial without understanding limits imposed by noise. Unfortunately, mere description of noise grows exponentially with system size, becoming cumbersome even for modest…
Error mitigation techniques are crucial to achieving near-term quantum advantage. Classical post-processing of quantum computation outcomes is a popular approach for error mitigation, which includes methods such as Zero Noise Extrapolation,…
Non-conservative uncertainty bounds are key for both assessing an estimation algorithm's accuracy and in view of downstream tasks, such as its deployment in safety-critical contexts. In this paper, we derive a tight, non-asymptotic…
A novel high-frequency market-making approach in discrete time is proposed that admits closed-form solutions. By taking advantage of demand functions that are linear in the quoted bid and ask spreads with random coefficients, we model the…
Despite decades of research and recent progress in adaptive control and reinforcement learning, there remains a fundamental lack of understanding in designing controllers that provide robustness to inherent non-asymptotic uncertainties…
Continuous quantum error correction has been found to have certain advantages over discrete quantum error correction, such as a reduction in hardware resources and the elimination of error mechanisms introduced by having entangling gates…
We propose methods to infer jumps of a semi-martingale, which describes long-term price dynamics, based on discrete, noisy, high-frequency observations. Different to the classical model of additive, centered market microstructure noise, we…
Variational Quantum Algorithms (VQAs) are a promising application for near-term quantum processors, however the quality of their results is greatly limited by noise. For this reason, various error mitigation techniques have emerged to deal…