Fast Monte-Carlo

TL;DR

This paper introduces an eigenvalue-based small-sample approximation for Markov Chain Monte Carlo that significantly reduces the number of paths needed while maintaining distributional accuracy and variance reduction.

Contribution

It presents a novel eigenvalue-based approach that drastically decreases Monte Carlo sample requirements from millions to tens without sacrificing accuracy.

Findings

Reduces Monte Carlo paths from 1,000,000 to as few as 10

Achieves comparable distributional results measured by Wasserstein distance

Provides significant variance reduction in steady-state distribution

Abstract

This paper proposes an eigenvalue-based small-sample approximation of the celebrated Markov Chain Monte Carlo that delivers an invariant steady-state distribution that is consistent with traditional Monte Carlo methods. The proposed eigenvalue-based methodology reduces the number of paths required for Monte Carlo from as many as 1,000,000 to as few as 10 (depending on the simulation time horizon $T$), and delivers comparable, distributionally robust results, as measured by the Wasserstein distance. The proposed methodology also produces a significant variance reduction in the steady-state distribution.