This study compares MC and QMC methods for derivative pricing, showing QMC's superior convergence rates.
problem Improving derivative pricing accuracy and efficiency in high-dimensional settings.
method Compared Monte Carlo and quasi-Monte Carlo techniques, focusing on convergence rates and low-discrepancy sequences.
result Quasi-Monte Carlo methods achieve superior convergence rates and reduce root mean square error in derivative pricing.
New algorithms improve MCMC efficiency for complex distributions.
problem High variance and low effective sample size in MCMC samplers.
method Antithetic Riemannian Manifold and Quantum-Inspired Hamiltonian Monte Carlo.
result Improved effective sample size and variance reduction.
New wavelets use Monte Carlo for efficient discretization.
problem Efficiently discretizing continuous wavelets on general domains.
method Defined continuous wavelets via spectral calculus and proposed a Monte Carlo discretization.
result Convergence of Monte Carlo wavelets under natural regularity assumptions.
New algorithms improve sampling from complex distributions.
problem Sampling from complex probability distributions efficiently.
method Regime-switching Langevin dynamics and Monte Carlo algorithms.
result Convergence guarantees and iteration complexities provided.
Combines normalizing flows and quasi-Monte Carlo for improved numerical integration.
problem Improving the efficiency of numerical integration methods.
method Uses normalizing flows to approximate distributions and quasi-Monte Carlo for sampling.
result Demonstrates an estimator with significantly lower variance.
Study Langevin Monte Carlo for sampling non-log-concave distributions.
problem Sampling from non-log-concave distributions, especially Gaussian mixtures.
method Discretizations of overdamped Langevin diffusions.
result Numerical simulations compare Langevin Monte Carlo algorithms' performance.
Speeds up complex portfolio exposure calculations.
problem Calculating exposure of portfolios with exotic derivatives.
method Least Squares Monte Carlo (LSMC) technique.
result Significantly reduces computation time for nested Monte Carlo.
GPU computing has become popular in computational finance and many financial institutions are moving their CPU based applications to the GPU platform. Since most Monte Carlo algorithms are embarrassingly parallel, they benefit greatly from parallel implementations, and consequently Monte Carlo has become a focal point …
Study compares MC and QMC methods for pricing and risk analysis in a hyperbolic local volatility model.
problem Derivative pricing and risk analysis in a hyperbolic local volatility model.
method Application of Monte Carlo and Quasi Monte Carlo methods for pricing and risk analysis.
result Quasi Monte Carlo methods show superior performance in high-dimensional integration for derivative pricing and risk analysis.
Paper analyzes and accelerates Langevin Monte Carlo methods using large deviations theory.
problem High-dimensional sampling problems in machine learning.
method Unified approach using large deviations theory to study and accelerate Langevin dynamics variants.
result Efficiency of Langevin dynamics variants demonstrated through numerical experiments.
New Monte Carlo method for fluctuating weight functions.
problem Stochastic weight functions in numerical studies.
method Construct a rigorous Monte Carlo algorithm with fluctuating weights.
result Algorithm visits points proportional to their average weight.
New Hamiltonian Monte Carlo method for non-canonical dynamics.
problem Incompatibility of canonical symplectic structure with non-canonical dynamics.
method Developed a framework for Hamiltonian Monte Carlo using non-canonical symplectic structures with implicit integration.
result Non-canonical Hamiltonian Monte Carlo provides sampling advantages.
A new method combines AIS and SMCI for efficient evaluation of Ising models.
problem Efficiently evaluating expectations on Ising models under various temperatures.
method Combining Annealed Importance Sampling (AIS) and Spatial Monte Carlo Integration (SMCI).
result The proposed method performs efficiently in both high- and low-temperature regions.
Estimates log marginal likelihood using multilevel Monte Carlo.
problem Estimating log marginal likelihood accurately.
method Unbiased multilevel Monte Carlo estimator.
result Validates application in variational Bayes.
Paper uses Monte Carlo simulations to predict retirement portfolios.
problem Retirement financial planning uncertainty.
method Monte Carlo simulations incorporating inflation, interest rates, etc.
result Probabilistic prediction of IRA and 401(k) values.
The paper proposes a new method to approximate Wasserstein-Fisher-Rao flows using Monte Carlo techniques.
problem Sampling from probability distributions and minimizing Kullback-Leibler divergence.
method Sequential Monte Carlo approximations of Wasserstein-Fisher-Rao gradient flows.
result The proposed method outperforms other Monte Carlo algorithms in certain conditions.
SLMC improves sampling efficiency for high-dimensional distributions.
problem Sampling from high-dimensional distributions is computationally challenging.
method SLMC projects Langevin updates onto subsampled eigenblocks of a time-varying preconditioner.
result SLMC offers superior adaptability and computational efficiency compared to traditional methods.
Study on Monte-Carlo dropout for uncertainty estimation in neural networks.
problem Variability in uncertainty estimation quality through Monte-Carlo dropout.
method Analysis of dropout behavior in neural networks.
result Observation of interesting properties for uncertainty estimation.
This paper improves portfolio market risk simulations using randomized quasi-Monte Carlo methods.
problem Simulating loss probabilities and conditional excesses for linear asset portfolios.
method Combines randomized quasi-Monte Carlo with importance sampling and stratified importance sampling.
result Quasi-Monte Carlo methods increase robustness of portfolio risk estimates.
This technical report is the union of two contributions to the discussion of the Read Paper "Riemann manifold Langevin and Hamiltonian Monte Carlo methods" by B. Calderhead and M. Girolami, presented in front of the Royal Statistical Society on October 13th 2010 and to appear in the Journal of the Royal Statistical Soc…
Recommender systems improve quantum Monte Carlo simulations.
problem Efficiency of quantum Monte Carlo methods without sacrificing accuracy.
method Quantum to classical mapping and molecular simulation techniques.
result Classical molecular gas model reproduces quantum distributions efficiently.
KMC uses gradient-free Hamiltonian Monte Carlo with efficient approximations for sampling.
problem Sampling from complex, intractable target densities.
method Adaptive MCMC based on Hamiltonian Monte Carlo with efficient kernel approximations.
result Substantial mixing improvements over gradient-free samplers.
Improved Hamiltonian Monte Carlo for Bayesian inference reduces variance and improves performance.
problem Efficiently sampling from posterior distributions in Bayesian inference with stochastic gradients.
method Variance reduction techniques applied to Hamiltonian Monte Carlo.
result Theoretical and experimental improvements in convergence and performance compared to variance-reduced Langevin dynamics.
Quantum algorithm speeds up financial option pricing.
problem Optimizing stopping times in stochastic processes for finance.
method Combines quantum computing techniques with LSM for optimal stopping.
result Achieves nearly quadratic speedup in runtime.
A new eigenvalue-based method speeds up Monte Carlo simulations.
problem Reducing the number of paths needed for accurate Monte Carlo simulations.
method Eigenvalue-based approximation of Markov Chain Monte Carlo.
result Significant variance reduction and comparable results to traditional Monte Carlo.
SBMC method improves uncertainty estimation in deep learning models.
problem Improving uncertainty quantification in deep learning models.
method A scalable Bayesian Monte Carlo method using a model and parallel SMC/MCMC algorithm.
result SBMC achieves comparable or better accuracy and improved uncertainty quantification compared to state-of-the-art methods.
SMC methods improve option pricing accuracy.
problem Approximating option prices via Monte Carlo methods.
method Constructing a sequence of artificial target densities and weighting functions.
result Significant gains in option pricing accuracy achieved.
This review aims to bridge the gap between MCMC users and geometric foundations.
problem Insufficient understanding of geometric tools in Hamiltonian Monte Carlo.
method Geometric tools and Hamiltonian dynamics for efficient probability density exploration.
result Comprehensive introduction to geometric tools accessible to non-experts.
Study improves sampling from complex distributions using annealed Langevin Monte Carlo.
problem Sampling from non-log-concave and multimodal distributions.
method Annealed Langevin Monte Carlo algorithm with theoretical guarantees.
result Oracle complexity of O(dβ²A²/ε⁶) for achieving ε² accuracy in Kullback-Leibler divergence.
The paper explores how control variates can reduce variance in Monte Carlo simulations, especially for Sobolev functions.
problem Efficiency of control variates in reducing variance for Monte Carlo simulations.
method Study of a specific quadrature rule using nonparametric regression-adjusted control variates.
result A specific quadrature rule can improve the Monte Carlo rate and achieve the minimax optimal rate under sufficient smoothness assumptions.
New methods improve efficiency of sampling algorithms for complex systems.
problem Efficiently sampling from complex, high-dimensional probability distributions.
method Randomized Runge-Kutta-Nyström methods tailored for Hamiltonian flows.
result Quantitative 5/2-order L2-accuracy in approximating Hamiltonian flows. This paper improves MCVI by using Quasi-Monte Carlo sampling to reduce gradient variance.
problem Reducing variance in Monte Carlo gradient estimators for faster convergence.
method Introducing Quasi-Monte Carlo (QMC) sampling to reduce variance in score function and reparameterization gradient estimators.
result The proposed QMC approach leads to faster convergence compared to standard Monte Carlo methods.
Stacked Monte Carlo improves option pricing efficiency.
problem Evaluating option prices in various models.
method A stacking technique that approximates Monte Carlo draws using a specified function.
result Shows efficiency in European and Asian Call options in both constant and stochastic volatility models.
Study non-asymptotic Langevin Monte Carlo for Gibbs distributions.
problem Sampling from Gibbs distributions with dissipative potentials.
method Langevin-type algorithms based on Liptser--Shiryaev theory and Poincaré inequalities.
result Upper bound on 2-Wasserstein distance for accurate approximation.
New method combines neural networks with Monte Carlo for complex system reliability.
problem Estimating small failure probabilities in complex systems.
method Subset Simulation with Hamiltonian Neural Networks.
result High acceptance rates and computational efficiency in low-probability regions.
In this paper we propose a flexible and efficient framework for handling multi-armed bandits, combining sequential Monte Carlo algorithms with hierarchical Bayesian modeling techniques. The framework naturally encompasses restless bandits, contextual bandits, and other bandit variants under a single inferential model. …
New method reduces Monte Carlo error in option pricing and Greeks estimation.
problem Reducing Monte Carlo error in option pricing and Greeks estimation.
method Denoised Monte Carlo technique for LSV models.
result Reduces Monte Carlo error by an order of magnitude.
New method reduces uncertainty in AI-driven Monte Carlo simulations.
problem Epistemic uncertainty in AI surrogate models affects Monte Carlo sampling outcomes.
method Penalty Ensemble Method (PEM) modifies Metropolis acceptance rule to increase rejection probability in uncertain regions.
result PEM enhances reliability of Monte Carlo simulations by reducing uncertainty propagation.
ParaMonte::Python streamlines Bayesian data analysis with fast Monte Carlo and MCMC routines.
problem Efficiently sampling posterior distributions in Bayesian modeling and data science.
method Serial and MPI-parallelized Markov Chain Monte Carlo (MCMC) routines.
result Automated model calibration and uncertainty quantification in Bayesian analysis.
In this paper, we discuss the application of quasi-Monte Carlo methods to the Heston model. We base our algorithms on the Broadie-Kaya algorithm, an exact simulation scheme for the Heston model. As the joint transition densities are not available in closed-form, the Linear Transformation method due to Imai and Tan, a p…
AFT combines AIS, SMC, and NFs for better Monte Carlo estimates.
problem Estimating normalizing constants of complex probability distributions.
method Annealed Flow Transport (AFT) integrates AIS, SMC, and normalizing flows.
result AFT improves Monte Carlo estimates of normalizing constants and expectations.
Deep learning enhances Hamiltonian Monte Carlo for sampling gauge field configurations.
problem Sampling from complex gauge field topologies efficiently.
method Stacked neural networks to generalize Hamiltonian Monte Carlo.
result Significantly reduces computational cost for generating gauge field configurations.
RQMC improves optimization in variational Bayes problems.
problem Optimizing variational Bayes problems with noisy objective functions.
method Use of randomized quasi-Monte Carlo (RQMC) sampling with stochastic L-BFGS.
result RQMC can significantly speed up optimization and find better parameter values.
Improves Monte-Carlo simulations for consistent mean and variance.
problem Artificial randomness in running mean calculations.
method Combining running mean and variance with accurate summing.
result Increased accuracy and robustness of Monte-Carlo estimates.
This paper extends AD techniques to Monte Carlo processes for efficient derivative calculation.
problem Obtaining derivatives of expectation values in Monte Carlo processes.
method Two approaches: reweighting and Hamiltonian extension of HMC.
result Hamiltonian approach as a change of variables simplifies variance reduction.
Consensus Monte Carlo clusters big data with shared anchors.
problem Clustering and feature allocation in large datasets.
method Bayesian nonparametric models, Dirichlet process, Indian buffet process, consensus Monte Carlo.
result Valid for various sampling models and priors.
New method combines Monte Carlo and tensor networks for solving complex equations.
problem Solving high-dimensional partial differential equations efficiently.
method Uses Monte Carlo simulations and tensor train sketching for updates and re-estimations.
result Demonstrates versatility and efficacy in solving specific equations.
Hamiltonian Monte Carlo converges to target distributions under mild conditions.
problem Establishing convergence of Hamiltonian Monte Carlo algorithms.
method Analyzing Lq convergence for Hamiltonian Monte Carlo under mild conditions. result Outputs converge to target distributions under specified conditions.