The Monte Carlo, filled with a lot of mystery is defined by Anderson et al (1999) as the art of approximating an expectation by the sample mean of a function of simulated variables. Used as a code word between Stan Ulam and John von Neumann for the stochastic simulations they applied to building better atomic bombs (Anderson, 1999), the term Monte Carlo evolved into a method used in a variety discipline including physic, finance, mechanics and even in areas such as town planning and demographic studies.
Monte Carlo methods are very different from deterministic methods (McLeish, 2004). In the case of a deterministic model the value of the dependent variable, given the explanatory variables, can only be unique value as given by a mathematical formula. This type of model contains no random components (Rotelli, 2015). In contrast, Monte Carlo does not solve an explicit equation, but rather obtains answers by simulating individual particles and recording some aspects (tallies) of their average behavior (Briesmeister, 2000). Given the broad applications and matters involving Monte Carlo Methods we will split this article into three parts to allow for a clear understanding. Read more