Genetic algorithm-based selection of optimal Monte Carlo simulations

The aim of this work is to propose the use of a genetic algorithm to solve the problem of the optimal subsampling of Monte Carlo simulations to obtain desired statistical properties. It is designed to optimally select the best m Monte Carlo simulations from a larger pool of N > m simulations. The concept of an “optimal selection” is defined through a target metric, in this work the first and second moments of the distribution, from the set of N simulations, to which the subset of m simulations should closely converge. The implementation employs an objective function, allowing the algorithm to balance computational efficiency and optimization performance, achieving fast and precise selection of the m simulations. • Novel Genetic Algorithm for Monte Carlo Subsampling : Introduces a genetic algorithm designed to optimally select a subset of Monte Carlo simulations, preserving key statistical properties such as mean and variance. • Efficiency in Simulation : The algorithm reduces computational time significantly by selecting a small, optimized subsample from a large pool of simulations, without compromising statistical accuracy. • Applications to Stochastic Processes : The approach is extended to various stochastic processes, including driftless Brownian motion, geometric Brownian motion, and the Ornstein–Uhlenbeck process, showcasing its flexibility. • Extension to Higher-Order Moments : The paper introduces an extension to optimize not just the first two moments (mean and variance), but also skewness and kurtosis, further improving the performance in financial simulations.