A deep learning model speeds up computation of numerous implied volatilities.
problem Frequent computation of numerous implied volatilities using iteration methods like Newton-Raphson reaches processing speed limits.
method Emulated Newton-Raphson method using PyTorch and optimized with TensorRT.
result Up to 1,000 times faster than a benchmark implementation of Newton-Raphson.
Improved bounds for Black-Scholes volatility lead to faster root-finding.
problem Finding accurate implied volatility for Black-Scholes model.
method Systematic use of option delta to derive tighter bounds, proposing a Newton-Raphson algorithm.
result Proposed algorithm converges rapidly for all price ranges, especially useful for extreme option prices.
Develops computational methods for simulating rigid body dynamics on SO(3).
problem Simulating rotational dynamics of rigid bodies on SO(3).
method Discrete Mechanics, Variational Integrators, Newton-Raphson algorithm.
result Preserves symplectic structure of SO(3) manifold dynamics.
Bayesian method speeds up demand forecasting for e-commerce.
problem Demand forecasting for fast and bursty items at scale.
method Approximate Bayesian inference using Newton-Raphson algorithm and Kalman smoothing.
result Significantly outperforms competing approaches on large datasets.
We introduce a new method of delta hedging. In many cases, this method results in a lower cost than the Black-Scholes method. To calculate the cost of hedging, we develop a Mathematica program that include the two-dimensional Newton-Raphson method.
Proposes a faster second-order method for MDPs.
problem Slow convergence of first-order value iteration methods in MDPs.
method Applies Newton-Raphson method to successive relaxation value iteration scheme.
result Second-order convergence and faster convergence to optimal solution.
Private minimum Hellinger distance estimators maintain robustness and efficiency while ensuring privacy.
problem Ensuring privacy in robust statistical estimation.
method Derive private minimum Hellinger distance estimators satisfying Hellinger differential privacy.
result Private minimum Hellinger distance estimators retain robustness and efficiency under privacy constraints.
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.
Unified framework for smooth convex regularization of optimal transport problems.
problem Optimizing transport plans with regularization.
method Unified framework based on matrix nearness problems with Bregman divergences.
result Regularized optimal transport equivalent to matrix nearness problem.
Consider a process, stochastic or deterministic, obtained by using a numerical integration scheme, or from Monte-Carlo methods involving an approximation to an integral, or a Newton-Raphson iteration to approximate the root of an equation. We will assume that we can sample from the distribution of the process from time…
Efficient oblique RSF method improves prediction and interpretability.
problem Limited computational efficiency and difficulty in interpreting oblique RSF ensembles.
method Newton-Raphson scoring for computational efficiency and negation importance for variable importance estimation.
result The method reduces computational overhead by 450 times and improves prediction accuracy.
Paper solves convertible bond valuation using finite elements with penalty method.
problem Valuation of convertible bonds under penalty TF model.
method Solves TF system of equations using P1 and P2 finite elements with penalty method.
result Numerical solutions compare favorably with finite difference method.
A new multivariate stochastic volatility estimation procedure for financial time series is proposed. A Wishart autoregressive process is considered for the volatility precision covariance matrix, for the estimation of which a two step procedure is adopted. The first step is the conditional inference on the autoregressi…
New method predicts neural network performance using free probability theory.
problem Stability and performance prediction of feed-forward neural networks.
method Free Probability Theory and homotopy method for Jacobian spectral density computation.
result FPT metrics correlate highly with final test accuracies of neural networks.
Complex volatility leads to chaotic fractals in option pricing.
problem Exploring the implications of complex volatility in Black-Scholes model.
method Analyzing the function for pricing European options with complex volatility and solving for implied volatility.
result Chaotic fractals emerge in the calculation of complex implied volatility.
A new method for robust product Markovian quantization overcomes numerical instabilities.
problem Numerical instabilities in the PMQ algorithm limit its adoption, especially for stochastic volatility models.
method Reformulated PMQ as standard vector quantization, applying accelerated Lloyd's algorithm for robustness.
result The method overcomes numerical instabilities and extends applicability to stochastic volatility models.
Transformer improves parameter estimation without needing closed-form solutions.
problem Parameter estimation in statistics, especially for complex distributions.
method Transformer-based approach for parameter estimation without closed-form solutions or derivations.
result Transformer-based approach achieves similar or better accuracy than maximum likelihood estimation.
In Neri and Schneider (2012) we presented a method to recover the Maximum Entropy Density (MED) inferred from prices of call and digital options on a set of n strikes. To find the MED we need to numerically invert a one-dimensional function for n values and a Newton-Raphson method is suggested. In this note we revisit …
Paper develops MMOT framework for financial applications with neural acceleration.
problem Financial optimization and calibration under multi-period martingale constraints.
method Theoretical analysis, incremental updates, adaptive sparse grids, hybrid neural-projection solver.
result Neural solver achieves 1597x speedup for real-time applications.
Estimates change points in Weibull time series with copulas.
problem Change-point estimation for nonlinear Weibull time series with copula-based Markov models.
method Copula-based Markov chain model with Weibull marginal distributions, incorporating asymmetric dependence structures through Clayton and Joe copulas.
result Proposed method performs well in estimating change points and model parameters, demonstrated through extensive numerical studies and empirical application.
Enhanced options trading strategies using advanced portfolio optimization.
problem Generating consistent positive returns in high-frequency options trading.
method Advanced portfolio optimization techniques applied to SPY options data.
result Sophisticated strategies incorporating advanced Greeks show potential in high-frequency trading.
Local laGPR speeds up multiscale mechanics simulations without neural networks.
problem High computational costs in multiscale mechanics simulations.
method Local approximate Gaussian process regression (laGPR) combined with FE schemes.
result laGPR offers better accuracy than neural networks for stress predictions.
Efficiently models categorical data with low to medium class overlap, improving accuracy over standard distributions.
problem Poor parameter estimates and accuracy in multinomial and Dirichlet multinomial distributions when assumptions are violated.
method Introduces Beta-Liouville multinomial distribution and efficient estimation methods.
result Beta-Liouville multinomial outperforms standard distributions on two out of four datasets.
NMC improves MCMC convergence by analyzing gradients to determine optimal proposal densities.
problem Improving MCMC convergence in structured relational models.
method Newtonian Monte Carlo (NMC) uses first and second order gradients to determine a suitable proposal density.
result NMC outperforms existing methods in various domains, including non-conjugate models.
FMOPF generates diverse near-optimal power flow solutions.
problem Generating diverse near-optimal power flow solutions for risk quantification.
method Decouples compression from generation through latent flow matching and explicitly models load-state coupling.
result FMOPF provides the most effective Newton-Raphson warm starts and lowest tail risk.
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.
We describe a novel optimization method for finite sums (such as empirical risk minimization problems) building on the recently introduced SAGA method. Our method achieves an accelerated convergence rate on strongly convex smooth problems. Our method has only one parameter (a step size), and is radically simpler than o…
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.
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.
In this paper, the author considers the numerical computation of CVA for large systems by Mote Carlo methods. He introduces two types of stochastic mesh methods for the computations of CVA. In the first method, stochastic mesh method is used to obtain the future value of the derivative contracts. In the second method, …
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.
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 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.
Recently, {\it stochastic momentum} methods have been widely adopted in training deep neural networks. However, their convergence analysis is still underexplored at the moment, in particular for non-convex optimization. This paper fills the gap between practice and theory by developing a basic convergence analysis of t…
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…
NCG methods improve shape optimization efficiency.
problem Shape optimization problems
method Nonlinear conjugate gradient methods
result NCG methods are efficient for shape optimization
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.
Various approaches to gene selection for cancer classification based on microarray data can be found in the literature and they may be grouped into two categories: univariate methods and multivariate methods. Univariate methods look at each gene in the data in isolation from others. They measure the contribution of a p…
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.