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Monte Carlo Method

## Definition

Monte Carlo Simulation, sometimes referred to as the Monte Carlo method, is a computerized mathematical technique that allows risk to be accounted for in quantitative analysis and decision making.

## Discussion

Risk analysis is an important part of almost every decision. However, many of those decisions are made in the face of uncertainty, ambiguity, and variability. Even though data and information upon which to make the decision might easily be available from multiple sources, the future cannot accurately be predicted and the ultimate outcome of the decision is still an unknown quantity. Monte Carlo simulation allows generation of all the possible outcomes of the decision before it is made, thus allowing the assessment of the impact of risk and allowing for better decision making in the face of uncertainty.

Monte Carlo simulation is a computerized mathematical technique that enables risk to be accounted for in quantitative analysis and decision making. A Monte Carlo simulation will provide the user with a range of possible outcomes and the probability of occurrence for each choice of action. In other words, it will show the potential consequence of both the most aggressive and the most conservative decision as well as providing the corresponding data for any "middle of the road" decision between the two extremes.

Early use of Monte Carlo simulation was made by scientists of the Manhattan Project - the development of the first atomic weapons during WWII - to help predict neutron penetration when they were investigating radiation shielding. Since then, it has been used in many applications in widely diverse fields such as finance, project management, energy, manufacturing, engineering, research and development, insurance, oil & gas, transportation, and the environment.

## How Monte Carlo Simulation Works

A Monte Carlo simulation performs a risk analysis of any chosen decision factor that has inherent uncertainty. It does this by building models of possible results using a probability distribution; that is, by substituting a range of values for any specific factor chosen by the decision maker. It then calculates the results numerous times, each time using a different set of random values from the probability functions. Depending upon the number of factors which are considered "uncertain" and the range of possible values specified for each of them, a Monte Carlo simulation could involve thousands, or even tens of thousands, of recalculations. The final products of a Monte Carlo simulation are distributions of possible outcome values.

By using probability distributions, variables can have different probabilities of different outcomes occurring. The probability distribution chosen for the simulation will depend upon the application under investigation. Common probability distributions include:

• Normal (bell curve) - The user defines the expected value (mean) and a standard deviation to describe the variation about that value.  The distribution is symmetrical and values in the middle (near the mean) are most likely to occur
• Lognormal – Values are not symmetrical as is the case in a Normal distribution. Rather, they are positively skewed.  A Lognormal distribution is used to represent values that will never fall below zero but have unlimited positive potential
• Uniform – All values have an equal chance of occurring. The user defines the minimum and maximum
• Discrete – The user defines a set of specific values that may occur as well as the likelihood of each

During a Monte Carlo simulation, values are sampled at random from the chosen probability distributions.  Each discrete sample set is referred to as an iteration and the resulting outcome from the calculations for that sample is recorded. A Monte Carlo simulation will repeat this process hundreds, thousands or even tens of thousands of times depending upon the complexity of the problem. The compiled result from all the iterations is a probability distribution of the possible outcomes that lie within the parameters chosen by the user.  A Monte Carlo simulation thus provides a comprehensive view of not only what could happen, but how likely it is to happen.

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