Dynamic tracking error framework shows similar performance but varying volatility across different constraints.
problem Differences in governance parameters between Total Portfolio Approach and Strategic Asset Allocation.
method Portfolio simulations using U.S. equity and bond data from 2000 to 2026, spanning 2004 to 2026.
result Realized tracking error volatility varies 12-fold across different constraints, with costs highest during crises.
New RL method improves financial index tracking accuracy.
problem Optimizing financial index tracking with dynamic market information.
method Discrete-time dynamic model, Banach fixed point iteration, deep reinforcement learning.
result Proposed RL method outperforms benchmarks in tracking accuracy.
Paper solves tracking control for (x,u)-flat systems using classical states.
problem Tracking control for (x,u)-flat systems. method Quasi-static feedback of classical states.
result Achieves linear, decoupled and asymptotically stable tracking error dynamics.
The efficiency of a modern economy depends on what we call the Value-Tracking Hypothesis: that market prices of key assets broadly track some underlying value. This can be expected if a sufficient weight of market participants are valuation-based traders, buying and selling an asset when its price is, respectively, bel…
Optimizes sliding window approach for tracking Gaussian densities.
problem Improving tracking performance of Gaussian density estimation.
method Theoretical analysis of sliding window Gaussian Kernel Density Estimators.
result Empirical evidence shows improved tracking performance with optimal weight sequence.
Perfect tracking control for real-world Euler-Lagrange systems is challenging due to uncertainties in the system model and external disturbances. The magnitude of the tracking error can be reduced either by increasing the feedback gains or improving the model of the system. The latter is clearly preferable as it allows…
DD algorithm tracks test error from train error without validation data.
problem Systematic generalization gap between train and test errors in modern model training.
method Decoupled descent (DD) algorithm that cancels data reuse biases via approximate message passing.
result DD algorithm rigorously demonstrates zero-cost validation and 100% data utilization.
PKF improves KF for dynamic uncertainty tracking in time-course data.
problem Dynamic uncertainty tracking in time-course data.
method Pathspace Kalman Filter (PKF) using Bayesian methodology.
result PKF outperforms conventional KF methods, reducing MSE by several orders of magnitude.
THRML uses energy-based models for index tracking, reducing portfolio tracking error and improving returns.
problem NP-hard combinatorial optimization in portfolio optimization under cardinality constraints.
method THRML reformulates index tracking as probabilistic inference on an Ising Hamiltonian, using GPU-accelerated block Gibbs sampling.
result THRML achieves 4.31 percent annualized tracking error compared to 5.66-6.30 percent for baselines, with 128.63 percent total return.
New approach uses Gaussian processes to learn and track complex systems with guaranteed accuracy.
problem Inaccurate first principle models for complex systems due to data complexity.
method Bayesian prediction error bound for Gaussian process regression, derived from kernel-based data density.
result Achieves vanishing tracking error with increasing data density, providing time-varying accuracy guarantees.
This paper describes a new online convex optimization method which incorporates a family of candidate dynamical models and establishes novel tracking regret bounds that scale with the comparator's deviation from the best dynamical model in this family. Previous online optimization methods are designed to have a total a…
High-probability bound for distributed stochastic approximation tracking error.
problem Analyzing the convergence of distributed stochastic approximation schemes.
method Analysis using ODE approach to stochastic approximation.
result High probability bound for tracking error between iterates and limiting differential equation.
Study efficient rebalancing strategies for portfolio tracking error.
problem Optimizing portfolio rebalancing under high-frequency asset price models.
method Discrete-time rebalancing strategies derived from continuous model.
result Asymptotically efficient sequence of simple strategies.
The paper provides guarantees for feedback control with sensor errors.
problem Certifying performance and safety in feedback control systems with sensor errors.
method Solving a supervised learning problem to characterize sensor errors and providing uniform error bounds.
result Finite-time convergence rate on sub-optimality of using a regressor in closed-loop for waypoint tracking.
SOOTT framework optimizes target tracking with robust and learning-augmented algorithms.
problem Optimizing target tracking in dynamic environments with adversarial perturbations.
method Integrates robust and learning-augmented algorithms for online decision-making.
result CoRT learning-augmented algorithm strictly improves over robust BEST when predictions are accurate.
This paper optimizes portfolio selection by penalizing tracking error, improving Sharpe ratio.
problem Optimizing portfolio allocation with a penalty for deviation from a reference portfolio.
method Formulated as a McKean-Vlasov control problem, provides explicit solutions and asymptotic expansions.
result The penalized portfolio strategy outperforms standard mean-variance and reference portfolios in most cases.
Bayesian deep learning improves seismic imaging uncertainty.
problem Uncertainty in seismic imaging due to data noise and linearization errors.
method Combines Bayesian inference and deep neural networks to quantify uncertainty in horizon tracking.
result Uncertainty in automatically tracked horizons can be quantified and visualized.
We study a series of static and dynamic portfolios of VIX futures and their effectiveness to track the VIX index. We derive each portfolio using optimization methods, and evaluate its tracking performance from both empirical and theoretical perspectives. Among our results, we show that static portfolios of different VI…
Momentum SGD fails to track nonstationary optima due to drift amplification.
problem Tracking nonstationary optima in stochastic optimization.
method Theoretical analysis of SGD and momentum variants under strong convexity and smoothness.
result Momentum incurs a drift-amplification penalty that diverges as the momentum parameter approaches 1, leading to systematic lag.
Bayesian approach for constructing and rebalancing sparse index-tracking portfolios.
problem Sparse tracking of a reference index with uncertainty quantification.
method Sparse linear regression with Laplace prior, empirical-Bayes calibration, Langevin-type MCMC, threshold-based rules.
result Posterior uncertainty on tracking error, portfolio composition, and rebalancing moves.
A DRL-based strategy improves vehicle tracking accuracy while saving energy.
problem Enhancing vehicle tracking accuracy in WSNs without increasing energy consumption.
method Decentralized strategy with dynamic reinforcement learning to adjust sensing areas.
result Simulation results demonstrate superior performance of DRL-aided design.
This paper develops nudging algorithms using learned surrogates for state estimation in dynamical systems.
problem Estimating the state of a dynamical system from partial observations when dynamics are unknown or expensive to simulate.
method Unified finite-dimensional analysis of nudging algorithms employing learned surrogate models of the dynamics.
result Nudging algorithms with surrogate models retain exponential convergence up to an explicit error floor.
This study models target trajectories using stochastic processes for efficient tracking.
problem Efficiently modeling and predicting target trajectories in continuous time.
method Decomposes trajectory modeling into deterministic and stochastic components using Gaussian or Student's-t processes. result Demonstrates superior performance in tracking maneuvering targets compared to existing methods.
HKF uses neural networks to adapt Kalman filters for dynamic channel tracking.
problem Tracking channels with varying dynamics and Doppler values.
method Combines Kalman filters with hypernetworks for dynamic adaptation.
result HKF achieves up to 2dB gain over Kalman filters at high Doppler values.
From human crowds to cells in tissue, the detection and efficient tracking of multiple objects in dense configurations is an important and unsolved problem. In the past, limitations of image analysis have restricted studies of dense groups to tracking a single or subset of marked individuals, or to coarse-grained group…
Passive investing can incur hidden costs due to market timing inefficiencies.
problem Hidden costs in passive investing due to market timing inefficiencies.
method Analysis of passive investing strategies, including gradual share acquisition and post-announcement trading.
result Post-announcement trading can earn significant profits, often exceeding 1%.
Optimizes decisions in time-varying distributions using online stochastic methods and Wasserstein distance.
problem Optimizing decisions in time-varying distributions using Wasserstein distance.
method Online proximal-gradient method, exact penalty method, constraint-tightening approach.
result Dynamic regret bounds for tracking and estimation error.
The paper analyzes constrained optimal portfolios in high dimensions using novel statistical learning techniques.
problem Forming optimal portfolios with constraints in high-dimensional asset spaces.
method CROWN method integrating factor models with nodewise regression for estimation in large dimensions.
result Demonstrates estimation consistency and convergence rates for constrained portfolio weights, risk, and Sharpe Ratio.
Mapping class group dynamics tracked through Teichmüller space.
problem Tracking mapping class group actions on Teichmüller space.
method Action on Teichmüller space and geometric intersection numbers.
result Effective estimate of mapping class group actions on Teichmüller space.
This paper studies the empirical tracking performance of leveraged ETFs on gold, and their price relationships with gold spot and futures. For tracking the gold spot, we find that our optimized portfolios with short-term gold futures are highly effective in replicating prices. The market-traded gold ETF (GLD) also exhi…
Missing value imputation is a fundamental problem in spatiotemporal modeling, from motion tracking to the dynamics of physical systems. Deep autoregressive models suffer from error propagation which becomes catastrophic for imputing long-range sequences. In this paper, we take a non-autoregressive approach and propose …
RL approach for target tracking with unknown dynamics and sensor control.
problem Tracking an unknown target with sensor control.
method Track-MDP formulation for RL, compared with POMDP.
result Optimal RL policy tracks all target paths with certainty.
Designing deterministic denominators for SGLD stabilizes large drifts.
problem Stabilizing large drifts in SGLD
method Using state-dependent envelopes and empirical quantiles for activation thresholds
result Proxy-quantile denominators are close to oracle-score behavior and improve deterministic taming choices
Partial (replication) index tracking is a popular passive investment strategy. It aims to replicate the performance of a given index by constructing a tracking portfolio which contains some constituents of the index. The tracking error optimisation is quadratic and NP-hard when taking the L0 constraint into account so …
Index tracking is a popular form of asset management. Typically, a quadratic function is used to define the tracking error of a portfolio and the look back approach is applied to solve the index tracking problem. We argue that a forward looking approach is more suitable, whereby the tracking error is expressed as expec…
This paper identifies and analyzes biases in risk-adjusted index weighting methods, affecting social welfare and market fairness.
problem Biases in risk-adjusted index weighting methods lead to tracking errors and fraud in indices and ETFs.
method Characterizes and analyzes the biases and adverse effects of risk-adjusted index weighting methods.
result These biases reduce social welfare and can enable harmful arbitrage activities.
RL policy tracks dynamic targets in partially known environments robustly.
problem Active target tracking in partially known environments.
method Deep reinforcement learning (RL) approach for in-sight tracking, navigation, and exploration.
result Unified RL policy shows robust behavior for agile and anomalous targets.
Two novel procedures track quantiles efficiently using an oracle.
problem Setting step size and tuning parameters for incremental quantile estimators.
method Estimate MSE, decompose into variance and bias, use oracle to select best estimator.
result Efficient quantile tracking with error close to theoretical optimum.
Bayesian methods improve tracking multiple objects through dynamic dependencies.
problem Tracking multiple objects with time-varying cardinality and unordered measurements.
method Employing Bayesian nonparametric models, specifically dependent Dirichlet and Pitman-Yor processes, for state estimation and Monte Carlo sampling for trajectory learning.
result The proposed methods outperform existing algorithms in estimating the time-varying number of objects and identifying object associations.
New framework tracks communities in dynamic networks.
problem Discovering and tracking communities in evolving networks.
method Spectral framework on Grassmann manifold for subspace tracking.
result Improved dynamic community detection results across various network types.
A spiral unibike track emerges from a mathematical construction.
problem Finding a unibike curve with a spiral shape.
method Starting with a polar square root curve, iteratively applying a differential equation to create a spiral unibike track.
result A spiral unibike curve is found with a precision error less than 10^-7.
The paper optimizes asset selection for index trackers and enhanced trackers with varying cardinality constraints.
problem Optimizing asset selection for index trackers and enhanced trackers with cardinality constraints.
method Divided into two steps: asset pre-selection and asset weight estimation. Used eight pre-selection procedures with different combinations of selection methods and regression types.
result Out-of-sample tracking errors are roughly proportional to 1/sqrt(cardinality). OLS is more effective than LAD, BE marginally more effective than FS, and (n) marginally more effective than (c).
Paper introduces EnDKF for more accurate pose tracking.
problem Accurate pose tracking with directional uncertainty.
method EnDKF integrates unit-quaternion attitude representation for better directional uncertainty capture.
result Significant reduction in error compared to traditional methods.
A novel tracking algorithm models dynamic objects as ellipsoids with time-varying orientation.
problem Tracking dynamic objects with time-varying orientation.
method Random matrix framework with variational Bayes for non-linear inference.
result The method outperforms state-of-the-art methods in accuracy and robustness.
In this paper, we are concerned with a non-asymptotic analysis of sampling algorithms used in nonconvex optimization. In particular, we obtain non-asymptotic estimates in Wasserstein-1 and Wasserstein-2 distances for a popular class of algorithms called Stochastic Gradient Langevin Dynamics (SGLD). In addition, the afo…
This paper addresses tracking of a moving target in a multi-agent network. The target follows a linear dynamics corrupted by an adversarial noise, i.e., the noise is not generated from a statistical distribution. The location of the target at each time induces a global time-varying loss function, and the global loss is…
In this work, we introduce a deep-structured conditional random field (DS-CRF) model for the purpose of state-based object silhouette tracking. The proposed DS-CRF model consists of a series of state layers, where each state layer spatially characterizes the object silhouette at a particular point in time. The interact…
Optimal portfolio tracking with dynamic capital injection into a ratcheting benchmark.
problem Optimizing a portfolio's performance by dynamically adding capital to a non-decreasing benchmark.
method Formulated as an unconstrained control problem with a running maximum cost, transformed into an auxiliary problem with a nonlinear HJB equation, solved using probabilistic representation and stochastic flow analysis.
result Established the existence of a unique classical solution to the HJB equation, providing feedback optimal portfolio strategies.