Related papers: Parallel American Monte Carlo
The famous least squares Monte Carlo (LSM) algorithm combines linear least square regression with Monte Carlo simulation to approximately solve problems in stochastic optimal stopping theory. In this work, we propose a quantum LSM based on…
We introduce an efficient numerical implementation of a Markov Chain Monte Carlo method to sample a probability distribution on a manifold (introduced theoretically in Zappa, Holmes-Cerfon, Goodman (2018)), where the manifold is defined by…
A new Monte Carlo algorithm for phase-space sampling, named (MC)**3, is presented. It is based on Markov Chain Monte Carlo techniques but at the same time incorporates prior knowledge about the target distribution in the form of suitable…
We consider Monte Carlo approximations to the maximum likelihood estimator in models with intractable norming constants. This paper deals with adaptive Monte Carlo algorithms, which adjust control parameters in the course of simulation. We…
In this paper we propose an efficient method to compute the price of multi-asset American options, based on Machine Learning, Monte Carlo simulations and variance reduction technique. Specifically, the options we consider are written on a…
Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster…
In this work, we introduce a Monte Carlo method for the dynamic hedging of general European-type contingent claims in a multidimensional Brownian arbitrage-free market. Based on bounded variation martingale approximations for…
The Monte Carlo algorithm is increasingly utilized, with its central step involving computer-based random sampling from stochastic models. While both Markov Chain Monte Carlo (MCMC) and Reject Monte Carlo serve as sampling methods, the…
With origins in game theory, probabilistic values like Shapley values, Banzhaf values, and semi-values have emerged as a central tool in explainable AI. They are used for feature attribution, data attribution, data valuation, and more.…
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…
Option valuation problems are often solved using standard Monte Carlo (MC) methods. These techniques can often be enhanced using several strategies especially when one discretizes the dynamics of the underlying asset, of which we assume…
The Picard-Lefschetz theory has been attracting much attention as a tool to evaluate a multi-variable integral with a complex weight, which appears in various important problems in theoretical physics. The idea is to deform the integration…
A pair of complementary algorithms are presented. One of the pair is a fast method for connecting graphs with an edge. The other is a fast method for removing edges from a graph. Both algorithms employ the same tree based graph…
We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to…
Extant "fast" algorithms for Monte Carlo confidence sets are limited to univariate shift parameters for the one-sample and two-sample problems using the sample mean as the test statistic; moreover, some do not converge reliably and most do…
We discuss two numerical methods, based on a path integral approach described in a previous paper (I), for solving the stochastic equations underlying the financial markets: the Monte Carlo approach, and the Green function deterministic…
This article presents a simple but effective and efficient approach to improve the accuracy and stability of Least-Squares Monte Carlo. The key idea is to construct the ansatz of conditional expected continuation payoff using the…
We consider convex stochastic optimization problems under different assumptions on the properties of available stochastic subgradient. It is known that, if the value of the objective function is available, one can obtain, in parallel,…
We propose and analyze a method for computing failure probabilities of systems modeled as numerical deterministic models (e.g., PDEs) with uncertain input data. A failure occurs when a functional of the solution to the model is below (or…
We develop the idea of using Monte Carlo sampling of random portfolios to solve portfolio investment problems. In this first paper we explore the need for more general optimization tools, and consider the means by which constrained random…