The risk has mathematically the expressed probability of approach of a certain event which is based on statistical data or expert evaluations and can be mathematically calculated.
Considering risk in terms of its assessment, it is necessary to solve the following problems:
- to describe as much as possible possible options of succession of events in the future corresponding to this risk (the possible result of decision making or casual events);
- to determine probabilities of approach of each of these options (casual events).
Probability of approach of an event (a probability measure of risk) can be determined by an objective or subjective method.
The objective method has the following versions:
- the direct method probabilistic (statistically) based on calculation of relative frequency to which there is a casual event: if in n tests the casual event is observed by m of times, then its probability is on a formula:
p = m / n
At the same time it is necessary to consider the following restrictions:
- pi = 1, that is the amount of probabilities of all events is equal to 1;
- 0 <= pi <1, the probability of a separate event has to be more or is equal 0 and less 1.
This method is the most preferable in that case when there is extensive and rather solid data about history of the evaluated object.
- the approximate probabilistic method is used when for some reason it is not possible to receive required distribution of probabilities by all options of succession of events.
A set of options try to simplify consciously in calculation that the received rough model was useful.
- indirect (qualitative) method. If use of exact or approximate probability of model is impracticable, then it is possible to be limited to measurement of some other indicators which are indirectly characterizing the considered risk and available to practical measurement.
This method gives only quality standard of risk.
The subjective method is based on use of the subjective criteria based on various assumptions; can treat them the judgment making the decision, its personal experience, assessment of the expert, consultant, etc.
Standard characteristics of risk are calculated on the basis of probabilities:
- mathematical expectation is the average all possible results where as scales probabilities of their achievement are used.
- dispersion - represents average of squares of deviations of a random variable from its mathematical expectation (i.e. deviations of the valid results from expected), a measure of spread
of rvadratny a root from dispersion is called standard deviation and shows degree of dispersion of possible project deliverables.
- the coefficient of a variation shows what share of mean value of a random variable its average dispersion is
- the correlation coefficient shows the communication between variables consisting in change of average size of one of them depending on changes another.
The criteria described above are applied to normal probability distribution since the analysis allows to simplify its major properties (symmetry of distribution of rather average, insignificant probability of big deviations of a random variable from the center of its distribution) significantly.
Methodical accounting of uncertain factors which distribution law is unknown is based on forming of special criteria (Wald's criterion, criterion of Sevidzha, Gurvits's criterion, Bayesa-Laplace's criterion, criterion of extreme optimism) on the basis of which decisions are made.