Since Giles introduced the multilevel Monte Carlo path simulation method [18], there has been rapid development of the technique for a variety of applications in computational finance. This paper surveys the progress so far, highlights the key features in achieving a high rate of multilevel variance convergence, and su…
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48 results for “Giles method”
A new method speeds up option valuation computations.
problem Computing option values efficiently with high accuracy.
method Multilevel Monte Carlo method.
result Significant speed-up in computations for higher accuracy.
Paper proves strong convergence of Ninomiya-Victoir scheme and proposes an improved multilevel estimator.
problem Strong convergence analysis of Ninomiya-Victoir scheme and optimization of multilevel Monte Carlo estimators.
method Proves strong convergence of order 1/2 for Ninomiya-Victoir scheme and proposes a modified scheme with strong coupling to Giles-Szpruch scheme.
result Improves efficiency of multilevel Monte Carlo estimators by reducing the number of discretization levels.
Motivated by weak convergence results in the paper of Takahashi and Yoshida (2005), we show strong convergence for an accelerated Euler-Maruyama scheme applied to perturbed stochastic differential equations. The Milstein scheme with the same acceleration is also discussed as an extended result. The theoretical results …
The multilevel Monte Carlo path simulation method introduced by Giles ({\it Operations Research}, 56(3):607-617, 2008) exploits strong convergence properties to improve the computational complexity by combining simulations with different levels of resolution. In this paper we analyse its efficiency when using the Milst…
Paper combines Vibrato and automatic differentiation for efficient financial option sensitivities.
problem Efficient computation of high-order derivatives for financial option sensitivities.
method Combines Vibrato and automatic differentiation methods.
result Combined method is faster and more stable than standard finite difference methods.
In usual stochastic volatility models, the process driving the volatility of the asset price evolves according to an autonomous one-dimensional stochastic differential equation. We assume that the coefficients of this equation are smooth. Using Itô's formula, we get rid, in the asset price dynamics, of the stochastic i…
A new weighted MLMC method improves efficiency in Monte Carlo simulations.
problem Improving efficiency in Monte Carlo simulations with correlated coarse level approximations.
method Generalization of MLMC to any number of levels with control variates and weights.
result Significant efficiency improvements possible, especially when coarse level approximations are poorly correlated.
Improved MLMC method for barrier options with non-Lipschitz coefficients.
problem Efficiency improvement for barrier option pricing with non-Lipschitz diffusion.
method Interpolated Drift Implicit Euler MLMC method, Lamperti transformation, Brownian bridge technique.
result Improved efficiency of MLMC for barrier options with non-Lipschitz coefficients.
Multilevel Monte-Carlo for computing the SCR with the standard formula and other stress testsq-fin.CP
Paper uses MLMC for SCR calculation and stress tests, showing computational efficiency.
problem Computing SCR and stress tests for insurance companies.
method Multilevel Monte-Carlo (MLMC) estimator for maximum of conditional expectations.
result MLMC estimator is computationally more efficient and avoids regression issues.
Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without Lévy area simulationq-fin.CP
In this paper we introduce a new multilevel Monte Carlo (MLMC) estimator for multi-dimensional SDEs driven by Brownian motions. Giles has previously shown that if we combine a numerical approximation with strong order of convergence with MLMC we can reduce the computational complexity to estimate expected value…
Improved iterative methods for risk parity portfolio weights.
problem Solving for portfolio weights in risk parity allocation.
method Enhanced CCD and Newton methods, including a rescaling step and improved initial guess.
result Improved CCD method is the best, three times faster with 40% fewer iterations.
Paper introduces stochastic mesh methods for efficient CVA computation.
problem Efficient computation of CVA for large systems using Monte Carlo methods.
method Introduces two stochastic mesh methods for CVA computation.
result Demonstrates the rate of convergence of the methods to real CVA values.
The study connects Gaussian quadrature methods to sigma-point methods in filtering and smoothing.
problem Understanding the relationship between Gaussian quadrature and sigma-point methods.
method Interpreting sigma-point methods as Gaussian quadrature methods with specific covariance functions, and discussing criteria for selecting sigma-point locations.
result Many sigma-point methods can be seen as Gaussian quadrature methods with specific covariance functions, and this interpretation extends to multivariate Gauss--Hermite integration methods and related spherical cubature rules.
A new method combines Laplace and Variational Bayes for scalable inference.
problem Complex models and large datasets make exact inference infeasible.
method Low-Rank Variational Bayes Correction (VBC) using Laplace method and Variational Bayes correction in a lower dimension.
result The method ensures scalability in both model complexity and data size.
Unified framework for model explanation methods based on feature removal.
problem Unclear relationships and preferences among various model explanation methods.
method Characterizes removal-based explanations along three dimensions.
result Unified 26 existing methods, including widely used approaches.
A new method speeds up optimization for sums, simpler than others.
problem Optimizing finite sums, especially in non-smooth cases.
method A novel accelerated method based on SAGA, with one parameter.
result Achieves accelerated convergence on strongly convex smooth problems.
Unified Convergence Analysis of Stochastic Momentum Methods for Convex and Non-convex Optimizationmath.OC
Unified analysis of momentum methods for deep learning.
problem Convergence analysis of stochastic momentum methods for convex and non-convex optimization.
method Developed a convergence analysis for two stochastic momentum methods.
result Unified framework revealing similarities and differences between methods.
This work reviews and evaluates methods for predicting prediction intervals in regression problems.
problem Calibration of prediction intervals in regression problems.
method Four classes of methods: Bayesian, ensemble, direct interval estimation, and conformal prediction.
result Conformal prediction can be used as a general calibration procedure.
Derives kernel PCA with Nyström method for scalability.
problem Scalability of kernel PCA.
method Nyström method for kernel PCA.
result Provides scalable alternative to full kernel PCA.
Develops a fast method for pricing American options under variance gamma model.
problem Inefficient methods for pricing American options under variance gamma model.
method Inspired by quadratic approximation method, uses machine learning on pre-calculated quantities to reduce error.
result Proposed method is efficient and accurate for practical use.
Pricing Derivatives under Multiple Stochastic Factors by Localized Radial Basis Function Methodsq-fin.CP
Two RBF methods solve complex financial derivatives pricing problems.
problem Pricing derivatives in models with multiple stochastic factors.
method Radial Basis Function Partition of Unity and Radial Basis Function generated Finite Differences methods.
result Both methods achieve high accuracy and are efficient for solving multi-dimensional PDEs.
New method combines spectral and sparse methods for Gaussian processes.
problem Efficiently fitting Gaussian processes to large datasets.
method Orthogonally decoupled variational Fourier features.
result Competitive performance on synthetic and real-world data.
Simple stochastic Newton and cubic Newton methods with fast convergence.
problem Minimizing large numbers of smooth and strongly convex functions.
method Stochastic Newton and cubic Newton methods with simple local linear-quadratic rates.
result Local linear-quadratic convergence results with fast adaptation to problem's curvature.
Improved spectral methods of moments for robust latent variable model learning.
problem Limited robustness of spectral methods of moments to model misspecification.
method Hierarchical approach using approximate joint diagonalization instead of tensor decomposition.
result Our method outperforms previous tensor decomposition methods in speed and model quality.
VAN method optimizes learning tasks with unified methods.
problem Optimizing learning tasks in active and reinforcement learning.
method Variational Adaptive-Newton method that unifies optimization, inference, and evolution strategies.
result VAN performs well on various learning tasks.
A Large-Scale Comparative Analysis of Imputation Methods for Single-Cell RNA Sequencing Dataq-bio.GN
A comprehensive benchmark of 15 scRNA-seq imputation methods across various datasets and analyses.
problem Imputation of single-cell RNA sequencing data to recover latent transcriptional signals.
method Evaluation of 15 imputation methods across 30 datasets and 6 downstream analyses.
result Traditional methods generally outperform DL-based methods in scRNA-seq data analysis.
New methods using natural gradient for structured optimization.
problem Structured optimization problems.
method Structured second-order methods via natural gradient descent.
result Efficiency demonstrated on non-convex and deep learning problems.
Improved A2C method with lower variance.
problem Reducing variance in deep policy gradient methods.
method Using control variate theory, derived a new A2C formulation with lower variance.
result New A2C method has lower variance and improved performance.
A new method speeds up deep neural network training.
problem Nonconvex optimization in deep neural networks.
method Scaled conjugate gradient method for nonconvex optimization.
result The method converges faster and achieves lower scores in practical applications.
We propose a new stochastic dual coordinate ascent technique that can be applied to a wide range of regularized learning problems. Our method is based on Alternating Direction Multiplier Method (ADMM) to deal with complex regularization functions such as structured regularizations. Although the original ADMM is a batch…
Hybrid method selects fewer genes for cancer classification.
problem Selecting genes for cancer classification from microarray data.
method Hybrid of univariate (LIK) and multivariate (RFE) feature selection methods.
result Hybrid method selects fewer genes with similar or better accuracy.
NCG methods improve shape optimization efficiency.
problem Shape optimization problems
method Nonlinear conjugate gradient methods
result NCG methods are efficient for shape optimization
Uncertainty Aware Trader-Company Method: Interpretable Stock Price Prediction Capturing Uncertaintyq-fin.CP
Proposes UTC method for stock price prediction with uncertainty quantification.
problem Lack of uncertainty estimates in stock prediction methods.
method Combines TC method with probabilistic modeling for point and uncertainty predictions.
result UTC method achieves higher returns and lower risks than baselines.
Survey of spectral, probabilistic, and deep metric learning methods.
problem Developing effective distance metrics for various machine learning tasks.
method Divided into spectral, probabilistic, and deep approaches, covering various techniques and their applications.
result Comprehensive overview of metric learning methods, including new developments and applications.
Geometric methods study 3-manifold splittings.
problem Studying Heegaard splittings of 3-manifolds.
method Geometric approaches.
result Recent advances in geometric methods.
A novel weighted feature selection method using fuzzy sets improves classification accuracy and stability.
problem Improving feature selection accuracy and stability in machine learning models.
method Combination of four feature selection methods using fuzzy sets and bootstrap.
result Our method achieved significantly higher stability than individual methods.
New method improves accuracy in computing implied volatility.
problem Computing implied volatility from the Black-Scholes model.
method Adaptive gradient descent optimizers for numerical computation.
result More accurate results compared to close form approximation and Newton-Raphson method.
The paper examines Wiener process for LID estimation methods.
problem Estimating local intrinsic dimension in high-dimensional datasets.
method Investigates recent LID estimation methods from a Wiener process perspective.
result Explains how methods behave under non-ideal conditions.
Discuss ML methods for economists, highlighting better performance in econometrics.
problem Applying ML methods to econometrics problems.
method Supervised and unsupervised learning methods, matrix completion, causal inference, optimal policy estimation.
result ML methods often outperform traditional econometric methods in specific econometrics problems.
New method detects business-relevant outliers in e-commerce conversion rates.
problem Identifying outliers in e-commerce conversion rate data.
method A novel unsupervised fluid IQR method that adjusts sensitivity based on platform activity.
result Fluid IQR method outperforms existing methods in business-relevance and robustness.
Saliency methods often misattribute predictions due to input transformations.
problem Saliency methods lack reliability when explanations are sensitive to non-contributing factors.
method Used a simple pre-processing step to demonstrate that transformations with no effect on the model can cause misleading attributions.
result Saliency methods that do not satisfy input invariance (mirror model sensitivity to input transformations) result in misleading attributions.
New method for faster optimization of convex functions.
problem Optimizing finite sums of smooth convex functions efficiently.
method Accelerated gradient descent combined with stochastic variance reduction in mini-batches.
result Achieves lower overall complexity and faster convergence rates.
The paper introduces admissible hierarchical clustering methods for asymmetric networks.
problem Characterizing and implementing hierarchical clustering methods for asymmetric networks.
method The paper characterizes admissible hierarchical clustering methods and proposes algorithms for their implementation.
result The paper describes three families of intermediate methods for admissible hierarchical clustering of asymmetric networks.
Medical image reconstruction advances from sparse models to machine learning.
problem Improving image quality and reducing noise in medical imaging.
method Iterative reconstruction, modified data acquisition methods, and machine learning models.
result Machine learning methods show promise in improving image quality.
R package for counterfactual explanation methods.
problem Lack of unified interfaces for counterfactual explanation methods.
method Developed a modular R6-based interface for three existing counterfactual methods and proposed extensions.
result Comparison of implemented methods' quality and runtime behavior.
Krylov Cubic Regularized Newton: A Subspace Second-Order Method with Dimension-Free Convergence Ratemath.OC
A new method for faster optimization in high dimensions.
problem Slow convergence in high-dimensional optimization problems.
method Subspace cubic regularized Newton method within Krylov subspace.
result Achieves a dimension-independent convergence rate of O(1/mk + 1/k^2).
Derives new optimization methods using variational integrators.
problem Optimization methods in machine learning.
method Variational integrators and principles of Hamilton and Lagrange-d'Alembert.
result Derives two families of optimization methods, including Nesterov's accelerated gradient method.