Monte Carlo Method

(redirected from Monte Carlo simulation)
Also found in: Dictionary, Thesaurus, Medical, Financial, Acronyms.

Monte Carlo method

[′män·tē ′kär·lō ‚meth·əd]
A technique which obtains a probabilistic approximation to the solution of a problem by using statistical sampling techniques.

Monte Carlo Method


a numerical method for solving mathematical problems using the modeling of random processes and events. The term “Monte Carlo method” was coined in 1949, although some calculations using the modeling of random events had been previously performed by statisticians. (The method is named after the city of Monte Carlo, which is well known for its Casino.) The Monte Carlo method gained wide-spread use only after the development of high-speed computers. Programs for carrying out calculations on computers using the Monte Carlo method are comparatively simple and, as a rule, do not require large-capacity internal memory.

Monte Carlo Method


a method in computational and applied mathematics based on the simulation of random variables and the construction of statistical estimates of desired values.

The Monte Carlo method is generally considered to have been formulated in 1944 by the American scientists J. von Neumann and S. Ulam. In connection with work on the development of atomic reactors, von Neumann and Ulam made extensive use of the apparatus of probability theory in the computer solution of applied problems. At first the Monte Carlo method was used primarily to solve complex problems of radiation transport theory and neutron physics for which traditional numerical methods were not suited. The method was subsequently applied to a large number of different problems in statistical mechanics. The method is now used in such areas as game theory, queuing theory, mathematical economics, and the theory of message transmission in the presence of interference.

To solve a deterministic problem by the Monte Carlo method, a probabilistic model is constructed, and the desired quantity, for example, a multidimensional integral, is represented as the mathematical expectation of a function of a stochastic process. The process is then simulated on a computer. Probabilistic models are known, for example, for the computation of integrals, the solving of integral equations of the second kind, the solving of systems of linear algebraic equations, the solving of boundary problems for elliptic equations, and the estimation of the eigenvalues of linear operators. An estimate with a low degree of error can be obtained by proper selection of the probabilistic model.

The simulation of random variables with given distributions plays a special role in various applications of the Monte Carlo method. Such simulation is generally done by transforming one or more independent values of a random number a that is uniformly distributed in the interval (0, 1). The sequences of sample values of a are usually obtained with a computer through the use of theoretical numerical algorithms, among which the residue method has become the most common. Such numbers are said to be pseudorandom; they are checked through statistical tests and the solution of standard problems.

If, in an estimate based on the Monte Carlo method, the random variables involved are determined by the actual process being simulated, then we speak of direct modeling. Such an estimate is inefficient if rare events are involved because the actual process contains little information about such events. This inefficiency is usually manifested in too large a probabilistic error (variance) of the random estimates of the desired quantities. Many techniques have been developed for reducing the variance of these estimates within the framework of the Monte Carlo method. Almost all the techniques are based on modifications of the simulation through the use of information on the function of the random variables whose expectation is being computed.

The Monte Carlo method has had, and continues to have, a considerable influence on the development of other methods of computational mathematics—for example, methods of numerical integration. The Monte Carlo method has been successfully used as a supplementary method in combination with other methods to solve many problems. (See also.)


Metod Monte-Karlo v problème perenosa izluchenii. Moscow, 1967.
Metodstatisticheskikh ispytanii (Metod Monte-Karlo). Moscow, 1962.
Reshenie priamykh i nekotorykh obratnykh zadach atmosfernoi optiki metodom Monte-Karlo. Novosibirsk, 1968.
Ermakov, S. M. Metod Monte-Karlo i smezhnye voprosy. Moscow, 1971.
Mikhailov, G. A. Nekotorye voprosy teorii metodov Monte-Karlo. Novosibirsk, 1974.


Monte Carlo method

A technique that provides approximate solutions to problems expressed mathematically. Using random numbers and trial and error, it repeatedly calculates the equations to arrive at a solution. Many of the Monte Carlo methods and practices used to be referred to as rather generic "statistical sampling." Monte Carlo, of course, is a historical reference to the famous casino in Monaco.
References in periodicals archive ?
Hence, the union of different techniques was proposed: Fuzzy numbers to represent certain types of uncertainties, stochastic processes to represent the others uncertainties and the Monte Carlo simulation to get approximate the real option value.
Advisers would be wise to add more questions to their due diligence checklist for Monte Carlo simulation software that includes: does the package contain normal or log-normal distributions; cross, serial and cross-serial correlation; standard deviations; and arithmetic or geometric average returns?
Thus, nearly all students need more time and experience to fully grasp the sampling distribution concept and other fundamental principles that I hope to illustrate through Monte Carlo simulation.
Monte Carlo simulation scheme as explained earlier was implemented to obtain the diffusely reflected light for a range of reduced scattering coefficient ([[micro].
99th percentile) that can be generated by a Monte Carlo simulation, for example, can shed light on the critical risks a company is exposed to, highlighting that firm's likeliest worst-case scenarios.
RISK by Palisade Corporation is a Monte Carlo simulation add-in for Microsoft Excel.
We have built finite-element models of the fields from such grids and run detailed Monte Carlo simulations of the complete electron-proton transport system.
A Monte Carlo simulation was produced to better understand CLAS's backward angle detection of K mesons produced from the phi meson photoproduction process.
A Monte Carlo simulation was applied to these three variables to allow forecasting a range of economic outcomes.
The latest version performs risk analysis on a spreadsheet using Monte Carlo simulation techniques.
These range from techniques as prosaic as cross-company interviews to establish a baseline for the understanding of risk and risk management practices throughout the firm, to complex Monte Carlo simulation models that provide rigorous quantitative analysis of the exposure resulting from virtually any type of single or combination risk.

Full browser ?