One can generate thousands, perhaps millions, of random sample paths, and look at the prevalent characteristics of some of their features. The assistance of the computer is instrumental in such studies. The glamorous reference to Monte Carlo indicates the metaphor of simulating the random events in the manner of a virtual casino. MonteCarlo
With no mathematical literacy we can launch a Monte Carlo simulation of an eighteen-year-old Christian Lebanese successively playing Russian roulette for a given sum, and see how many of these attempts result in enrichment, or how long it takes on average before he hits the obituary. We can change the barrel to contain 500 holes, a matter that would decrease the probability of death, and see the results. Monte Carlo simulation methods were pioneered in martial physics in the Los Alamos laboratory during the A-bomb preparation. They became popular in financial mathematics in the 1980s, particularly in the theories of the random walk of asset prices. MonteCarlo
Monte Carlo methods, in brief, consist of creating artificial history. MonteCarlo
Stochastic processes refer to the dynamics of events unfolding with the course of time. Stochastic is a fancy Greek name for random. This branch of probability concerns itself with the study of the evolution of successive random events —one could call it the mathematics of history. The key about a process is that it has time in it. Stochastic MonteCarlo History
The evolutionary way of thinking taught by my Monte Carlo simulators. MonteCarlo Evolution Darwin
I became addicted to the various Monte Carlo engines, which I taught myself to build, thrilled to feel that I was generating history, a Demiurgus. It can be electrifying to generate virtual histories and watch the dispersion between the various results. Such dispersion is indicative of the degree of resistance to randomness. MonteCarlo History
I have two ways of learning from history: from the past, by reading the elders; and from the future, thanks to my Monte Carlo toy. MonteCarlo History
The invisible histories have a scientific name, alternative sample paths, a name borrowed from the field of mathematics of probability called stochastic processes. The notion of path, as opposed to outcome, indicates that it is not a mere MBA-style scenario analysis, but the examination of a sequence of scenarios along the course of time. We are not just concerned with where a bird can end up tomorrow night, but rather with all the various places it can possibly visit during the time interval. MonteCarlo