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Business planning. Monte Carlo method (most important)

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48. MONTE CARLO METHOD

Purpose of statistical analysis - determine the degree of impact of random factors on project performance indicators.

The analysis is carried out as follows. Let us assume that it has been determined which data should be considered uncertain, and also a range of values ​​within which they can vary randomly has been established. If we are talking, for example, about two parameters, this means that the range of values ​​of the source data has been defined, having the shape of a rectangle. For three variables, this region is a parallelepiped. The set of initial data on which the fate of the project depends is displayed by a point lying inside the selected area. There are a great many such points, so it is impossible to perform project calculations for each of them. However, it is necessary to determine what effect the uncertainty of the input data has on the behavior of the model. This problem is solved using the Monte Carlo method.

Suppose we have a way to select points in a selected data area randomly, similar to roulette in a gambling establishment. For each point chosen in this way, we will calculate the performance indicators and write them down in a table. Having done a sufficiently large number of experiments, we can draw some conclusions.

Two criteria are used to quantify the results. mean value and uncertainty. Suppose we have done N experiments and obtained a set of values ​​for some indicator f(n = 1, N). Then the average value of M is determined by the formula

where M is the expected value of fn; f - a certain indicator under study; N is the number of experiments performed.

The uncertainty (or coefficient of variation) is calculated as follows:

The value M can be interpreted as the expected value of the random variable fn.

Uncertainty can also be viewed as an assessment of the risk associated with the fact that the value of fn deviate from the expected value of M.

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