# A Comprehensive Methodology for Investment Project Assessment Based on Monte Carlo Simulation
## Materials and Methods
### Methodology for Investment Assessment
If historical data are available, on the basis of these data the stochastic nature of the variables can be transformed into a suitable distribution function (via the FIT function), and it is then advisable to use this option. However, there is not always a sufficient amount of data, or they are of such a nature that the distribution function cannot be \"fitted\". Then it is necessary to define the distribution function. It is based on history, trends, forecasts, etc. The basis is also a result of the analysis from the previous phase. There are different functions to choose for both discrete and continuous variables. The reliability of the simulation result directly depends on the type and accuracy of the probability distribution estimate. This activity should be performed on the basis of an expert assessment by a qualified employee. Figure 1: A comprehensive procedure for assessing an investment problem. In many cases, the input risk variables are statistically dependent on real conditions and their impact on the output is influenced by this. In such a case, it is necessary to specify the correlation between the inputs, usually in the form of a correlation matrix. In practice, this is, for example, the correlation of the variables product price and sales volume, which represent input variables with a negative correlation (an increase in price reduces demand). This establishes a stochastic financial model. _The simulation process._ The simulation process consists of a large number of simulation steps that are repeated until the end of the simulation, determined by the number of repetitions or the specified accuracy of the results. Each simulation step generates random values of risk factors, and the average value of the output quantity--the financial criteria--is subsequently calculated from their probability distribution. Depending on the type of simulation program, other simulation parameters are also defined in this phase, such as the type of simulation technique, the simulation speed, the expected output target value, lower and upper tolerance, or the form of displaying the simulation results. Simulation outputs are presented graphically and tabularly. _Evaluation of simulation outputs._ The simulation outputs, the average value of the simulated output quantity, including its probability profile and the impact of risk factors, are assessed against the established goals and risk criteria. If the value of the simulated variable or its reliability is out of tolerance, optimization should be considered. If the simulation outputs are acceptable with respect to the value and reliability of the simulated variable, the impacts of the risk factors are assessed against the established risk criteria. If the risk factors are assessed as unacceptable, according to their severity, it is necessary to propose measures to reduce the risk of achieving the target. From the output of the simulation, it is possible to determine the severity of individual risk factors in terms of their impact on the output, how they affect the value of the output (or the probability of achieving the goal), and how they affect the risk of the output (usually represented by the standard deviation). 3 rd step: Optimization. The goal of optimization is to find the optimal solution for the monitored problem using a simulation model. Most of the software uses the optimization tool OptQuest, which allows for the combination of classical linear programming and optimization under uncertainty. Before starting the optimization itself, in addition to the uncertain input variables, it is necessary to define the output quantity and the decision variables. Optimization follows at least one standard simulation cycle, and the reason for optimization is when the output does not meet expectations, requirements, or limitations. Optimization starts by setting the optimization goal. A goal refers to an output quantity and is most often defined as a requirement to maximize or minimize its average value. However, it is not a rule.