Fast Monte-Carlo
For practitioners of Monte Carlo simulation, this method dramatically reduces computational cost while preserving distributional robustness.
This paper introduces an eigenvalue-based approximation of Markov Chain Monte Carlo that reduces the required number of simulation paths from 1,000,000 to as few as 10 while maintaining comparable accuracy in Wasserstein distance and achieving significant variance reduction.
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.