The need for parameter estimation with massive datasets has reinvigorated interest in stochastic optimization and iterative estimation procedures. Stochastic approximations are at the forefront of this recent development as they yield procedures that are simple, general, and fast. However, standard stochastic approxima…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
Trend · papers per month
48 results for “numerical procedure”
The first part of this paper discusses general procedures for finding numerical approximations to distinguished Kahler metrics, such as Calabi-Yau metrics, on complex projective manifolds. These procedures are closely related to ideas from Geometric Invariant Theory, and to the asymptotics of high powers of positive li…
Concave regularization methods provide natural procedures for sparse recovery. However, they are difficult to analyze in the high dimensional setting. Only recently a few sparse recovery results have been established for some specific local solutions obtained via specialized numerical procedures. Still, the fundamental…
Efficiently calculates Brazilian stock options with discrete dividends.
problem Accurately pricing Brazilian listed equity options with discrete dividends.
method Uses the fast Laplace transform for high-accuracy computation.
result Efficiently computes option premiums and Greeks with high accuracy.
We simplify SVI volatility smile constraints for three sub-SVIs without numerical methods.
problem No arbitrage constraints for SVI volatility smiles.
method Explicit domain derivation for sub-SVIs without numerical procedures.
result Explicit no arbitrage domains for Symmetric SVI, Vanishing Upward/Downward SVI, and SSVI.
We develop a mixture procedure for multi-sensor systems to monitor data streams for a change-point that causes a gradual degradation to a subset of the streams. Observations are assumed to be initially normal random variables with known constant means and variances. After the change-point, observations in the subset wi…
Iterative procedures for parameter estimation based on stochastic gradient descent allow the estimation to scale to massive data sets. However, in both theory and practice, they suffer from numerical instability. Moreover, they are statistically inefficient as estimators of the true parameter value. To address these tw…
The paper analyzes numerical instability in variational flows and proposes a diagnostic method.
problem Numerical instability in variational flows affects sampling, density evaluation, and ELBO estimation.
method Treated variational flows as dynamical systems, used shadowing theory for theoretical guarantees, and developed a diagnostic procedure.
result Despite numerical instability, results from variational flows can be accurate enough for practical applications.
In this paper, we investigate a numerical algorithm for the pricing of swing options, relying on the so-called optimal quantization method. The numerical procedure is described in details and numerous simulations are provided to assert its efficiency. In particular, we carry out a comparison with the Longstaff-Schwartz…
DNA-SE uses deep learning to solve semiparametric problems efficiently.
problem Solving semiparametric integral equations in high dimensions.
method Formulates semiparametric estimation as a bi-level optimization problem and uses DNN to approximate solutions.
result Demonstrates numerical and statistical advantages over traditional methods.
Method detects errors in numerical data using regression models.
problem Noise and errors in numerical datasets.
method Introduced veracity scores and a filtering procedure for error detection.
result Method outperforms other approaches in identifying incorrect values.
New OCBA procedures minimize PICS in robust R&S.
problem Selecting the best alternative under input uncertainty.
method Developed new asymptotically optimal OCBA procedures.
result Procedures minimize probability of incorrect selection.
New boundary condition for Black-Scholes equations in strict local martingale models.
problem Computing prices of European options with underlying asset as a strict local martingale.
method Numerical procedure using finite difference methods with a new boundary condition at infinity.
result The minimal solution, satisfying a discrete maximum principle, is the correct derivative price.
Deep neural networks and the ENO procedure are both efficient frameworks for approximating rough functions. We prove that at any order, the ENO interpolation procedure can be cast as a deep ReLU neural network. This surprising fact enables the transfer of several desirable properties of the ENO procedure to deep neural…
The dying ReLU refers to the problem when ReLU neurons become inactive and only output 0 for any input. There are many empirical and heuristic explanations of why ReLU neurons die. However, little is known about its theoretical analysis. In this paper, we rigorously prove that a deep ReLU network will eventually die in…
We consider a structural model where the survival/default state is observed together with a noisy version of the firm value process. This assumption makes the model more realistic than most of the existing alternatives, but triggers important challenges related to the computation of conditional default probabilities. I…
We introduce a new method for estimating the parameter of the bivariate Clayton copulas within the framework of Algorithmic Inference. The method consists of a variant of the standard boot-strapping procedure for inferring random parameters, which we expressly devise to bypass the two pitfalls of this specific instance…
Boosts change-point detection power with optimal sub-sampling.
problem Power loss in sequential change-point detection from large history data.
method Optimal sub-sampling of history data before kernel-based detection procedures.
result Improved detection performance in extensive experiments.
Optimizes Gaussian process hyperparameters using Bayesian autoregression.
problem Optimizing hyperparameters for Matérn kernel temporal Gaussian processes.
method Recursive Bayesian estimation for autoregressive parameters.
result Outperforms traditional optimization methods in runtime and accuracy.
We provide a rigorous numerical computation method to validate periodic, homoclinic and heteroclinic orbits as the continuation of singular limit orbits for the fast-slow system with one-dimensional slow variable . Our validation procedure is based on topological tools called isolatin…
We show that the jumps correlation matrix of a multivariate Hawkes process is related to the Hawkes kernel matrix through a system of Wiener-Hopf integral equations. A Wiener-Hopf argument allows one to prove that this system (in which the kernel matrix is the unknown) possesses a unique causal solution and consequentl…
A new distribution addresses scalability and numerical stability issues of the vMF.
problem Scalability and numerical stability issues in sampling from the von Mises-Fisher (vMF) distribution.
method Proposes the Power Spherical distribution, retaining vMF's properties but addressing its drawbacks.
result Demonstrates the stability of Power Spherical distributions and applies it to a variational auto-encoder.
Reference metrics are used to define the differential structure on multicube representations of manifolds, i.e., they provide a simple and practical way to define what it means globally for tensor fields and their derivatives to be continuous. This paper introduces a general procedure for constructing reference metrics…
Myopic procedures are shown to be asymptotically optimal in ranking and selection problems.
problem Selecting the best design from a set with unknown mean performance.
method Myopic procedures that iteratively improve an approximation of the objective measure.
result Myopic procedures satisfy optimality conditions of ranking and selection problems.
A novel formulation and training procedure for full Boltzmann machines in terms of a mixed binary quadratic feasibility problem is given. As a proof of concept, the theory is analytically and numerically tested on XOR patterns.
We study a logistic model-based active learning procedure for binary classification problems, in which we adopt a batch subject selection strategy with a modified sequential experimental design method. Moreover, accompanying the proposed subject selection scheme, we simultaneously conduct a greedy variable selection pr…
We propose an efficient lattice procedure which permits to obtain European and American option prices under the Black and Scholes model for digital options with barrier features. Numerical results show the accuracy of the proposed method.
New method uses image registration to recover complex signals from amplitude data.
problem Recovering complex-valued signals from amplitude measurements.
method Indirect registration using LDDMM formalism with exterior calculus.
result Algorithm performs well under various conditions including noise and topology.
We solve for functions from their truncated Hilbert transforms using Chebyshev series.
problem Finding functions from their truncated Hilbert transforms.
method Express functions in Chebyshev series and numerically estimate coefficients.
result Numerical methods work well for extrapolating functions from truncated Hilbert transforms.
Investigation of the market graph attracts a growing attention in market network analysis. One of the important problem connected with market graph is to identify it from observations. Traditional way for the market graph identification is to use a simple procedure based on statistical estimations of Pearson correlatio…
Improves numerical solution of ill-conditioned linear systems for machine learning.
problem Wastefulness and instability in solving ill-conditioned linear systems.
method autonugget combines Richardson extrapolation to determine the solution of the ill-conditioned system, improving accuracy over a single nugget.
result Improves accuracy of numerical solution of ill-conditioned linear systems.
A procedure for unfolding the true distribution from experimental data is presented. Machine learning methods are applied for simultaneous identification of an apparatus function and solving of an inverse problem. A priori information about the true distribution from theory or previous experiments is used for Monte-Car…
The paper offers a unified approach to the study of three locally adaptive estimation methods in the context of univariate time series from both theoretical and empirical points of view. A general procedure for the computation of critical values is given. The underlying model encompasses all distributions from the expo…
We consider stochastic volatility models using piecewise constant parameters. We suggest a hybrid optimization algorithm for fitting the models to a volatility surface and provide some numerical results. Finally, we provide an outlook on how to further improve the calibration procedure.
A new scheme for FBSDEs simplifies computation without Monte Carlo.
problem Numerical solution for decoupled FBSDEs with reduced complexity.
method Recursive marginal quantization for fully quantization-based scheme.
result Effective numerical procedure for financial applications.
Discretization of Dirac systems and port-Hamiltonian systems: the role of the constraint algorithmmath.NA
Study discretizes Dirac and port-Hamiltonian systems using manifolds.
problem Discretization of Dirac and port-Hamiltonian systems.
method Retraction and discretization maps on manifolds for Dirac structures, applied to port-Hamiltonian systems.
result Numerical integrators for port-Hamiltonian systems derived from discretization techniques.
A new method for handling imbalanced data in regression models.
problem Imbalanced data in regression models with continuous or discrete covariates.
method Combines weighted resampling and data augmentation procedures.
result Improves the accuracy of model estimates by addressing imbalanced data.
Proposes diffusion models using mixed Gaussian priors for better data representation.
problem Improving data representation in diffusion models.
method Structured diffusion models with a mixture of Gaussians as prior.
result Improved model performance compared to classical diffusion models.
Optimal ridge regularization computed iteratively from generative parameters.
problem Finding the optimal ridge regularization strength for linear regression.
method Iterative procedure to compute optimal regularization strength numerically.
result The proposed procedure attains near-optimal generalization across various conditions.
New method detects changes online with bounds on delay.
problem Detecting changes in data streams efficiently.
method Maximizes discrepancy between pre-change and post-change distributions.
result Non-asymptotic bounds on average running length and detection delay.
We consider indifference pricing of contingent claims consisting of payment flows in a discrete time model with proportional transaction costs and under exponential disutility. This setting covers utility maximisation as a special case. A dual representation is obtained for the associated disutility minimisation proble…
Study simulates Variance Gamma processes for energy derivatives pricing.
problem Simulating Variance Gamma processes for accurate energy derivative pricing.
method Three-step procedure to relate self-decomposability to increments, derived from Qu et al. (2019). Exact simulation of skeleton of Variance Gamma and symmetric Variance Gamma driven Ornstein-Uhlenbeck processes.
result Exact simulation of Variance Gamma and related processes without numerical inversion.
Sketch Tomography improves quantum state estimation accuracy.
problem Efficiently estimating quantum states, especially MPS states.
method Hybridizes classical shadow protocol with tensor train ansatz.
result Proven convergence with quadratic sample complexity.
Community detection is a fundamental statistical problem in network data analysis. Many algorithms have been proposed to tackle this problem. Most of these algorithms are not guaranteed to achieve the statistical optimality of the problem, while procedures that achieve information theoretic limits for general parameter…
We consider the classical problem of building an arbitrage-free implied volatility surface from bid-ask quotes. We design a fast numerical procedure, for which we prove the convergence, based on the Sinkhorn algorithm that has been recently used to solve efficiently (martingale) optimal transport problems.
Proposes cost-sensitive feature selection for SVMs.
problem Asymmetric misclassification costs in feature selection.
method Mathematical optimization-based approach for SVMs.
result Substantial reduction in feature count with desired error rates.
Considering that a trader or a trading algorithm interacting with markets during continuous auctions can be modeled by an iterating procedure adjusting the price at which he posts orders at a given rhythm, this paper proposes a procedure minimizing his costs. We prove the a.s. convergence of the algorithm under assumpt…
The convolution method for the numerical solution of forward-backward stochastic differential equations (FBSDEs), introduced in [21], uses a uniform space grid. In this paper we utilize a tree-like spatial discretization that approximates the BSDE on the tree, so that no spatial interpolation procedure is necessary. In…