# Evaluation of Investments in Wind Energy Projects, under Uncertainty. State of the Art Review
## 4 Results Analysis
### Evaluation of Real Options and Modeling of Uncertainties
Geometric Brownian Motion, used in 61.3% (19) of the studies, is a stochastic process in continuous time, generated from a transformation of a standard Wiener process, with the particularity of not allowing asset prices to take negative values [145]. Geometric Brownian Motion appears to be better suited to long-term energy-related investments [146]. 2. Reversal of the mean indicates that values, such as prices, may move away from the mean or intrinsic value, but, over time, they will eventually return to those mean values [147]. 3. The Weibull distribution is the probability function that best describes the wind speed path, thanks to the orthogonal composition of two correlated Gaussian functions. The Weibull density function consists of two parameters: one refers to the  
Figure 12: Real options valuation techniques. maximum speed and the other indicates the degree of dispersion of the samples ([PERSON] et al., 2009). 4. The Box-Jenkins and Ornstein-Uhlenbeck model is the basis of all modern time series analysis theory, and consists of the analysis of probabilistic or stochastic properties of economic time series where the endogenous variable (Yt) is explained by past values or lags of itself and by stochastic error terms (148). 5. The ARIMA distribution is an econometric methodology based on dynamic models using time series data, made up of three components: the autoregressive (AR), the integration (I), and the moving average (MA), represented by the parameters p, \(d\), and q, respectively. The model includes the values of the series, prediction of errors, and a random term (149). 6. The normal distribution is a mathematical model that allows determining probabilities of occurrence for different values of the variable. The graph of the normal distribution has the shape of a bell, and for this reason it is also known as the Gaussian bell, whose central elements are the mean and the variance (150). 7. Markov chains are discrete stochastic processes used to study the evolution of certain systems in repeated trials, in which the probability of an event occurring depends only on the immediately preceding event. Transition probabilities are used to describe the way the system passes to the next state. There are also non-random uncertainty modeling techniques, the binomial model of [PERSON], [PERSON], and [PERSON], used to model non-random uncertainties in discrete time, and learning curves, used to model technological uncertainty. This concept was generated from a study by [PERSON] (1936), where he analyzes repetitive production in the construction of airplanes, finding, as a hypothesis, that \"the man-hours necessary to complete a production unit would decrease in a constant percentage each time the production doubles\" (151), showing that the repetitive action of a process increases the experience and learning on the part of the operator, managing to reduce the production time per unit (152). Figure 13 shows the techniques used to model the uncertainties studied. They are grouped in two blocks. In the upper part, there are the random techniques, and in the lower part, the non-random ones. It can be seen that the researchers opt for random techniques, preferably Geometric Brownian Motion (GBM), which is consistent with the type of uncertainty considered in the studies, which are mostly continuous, such as electricity prices and wind conditions. Both in evaluating real options and in modeling uncertainties, a standard pattern has not been followed when developing the models, regarding the type and number of  
Figure 13: Uncertainty modeling techniques. techniques to be used, which indicates that, without exception, techniques are combined according to the purpose and scope of each particular study, as seen in Table 6.