The Monte Carlo method is a statistical technique that utilizes randomness to solve mathematical problems. It was developed in the 1940s by mathematician Stanislaw Ulam and is named after the gambling town of Monte Carlo, as its principles resemble games of chance like roulette. This method is particularly effective for quantifying risk and is widely used in various fields, including finance, sales forecasting, and predictive modeling ³.

Monte Carlo simulations work by generating random samples to approximate complex quantities without needing to solve the system analytically. The core idea is that a point in a moving system will eventually explore all parts of the space uniformly and randomly, a property known as ergodicity. This allows for the evaluation of probabilities and functions in a stochastic manner ³⁴.

There are different classes of Monte Carlo sampling, including direct sampling, importance sampling, and rejection sampling. These methods can be applied to optimization problems and the evaluation of complex probabilities ⁴.