Risk analysis methods

Now the most effective is an integrated approach to risk analysis. On the one hand, such approach allows to gain a better understanding about possible results of project implementation, i.e. about all positive and negative surprises expecting the investor, and on the other hand, does possible broad application of mathematical methods (in particular probabilistic and statistical) for risk analysis.

In the theory of risks allocate the following types of mathematical models: direct, the return and research problems of sensitivity. In direct tasks the risk assessment connected with determination of its level occurs on the basis of a priori known information. In the return tasks restrictions for one or several varied initial parameters for the purpose of satisfaction of the set restrictions for the level of acceptable risk are set. The main idea of a method of the research of sensitivity applied in connection with inevitable inaccuracy of initial information consists in the analysis of vulnerability, degree of convertibility of productive indicators in relation to variation of parameters of models (distribution of probabilities, areas of change of these or those sizes, etc.). Conclusions of a research of sensitivity of the investment project reflect degree of reliability of the project results received in the analysis. In case of their unauthenticity the analyst will be forced to realize one of the following opportunities:

• to specify parameters which inaccuracy is the most essential in distortion of result;
• to change methods of processing of basic data for the purpose of reduction of sensitivity of the answer;
• to change a mathematical model of the analysis of project risks;
• to refuse carrying out quantitative risk analysis of the project.

The following classes of mathematical models considering uncertainty and differing on methods of its description are widely applied to the analysis of investment projects:

• stochastic models;
• linguistic models;
• not stochastic (game) models.

It is possible to classify existing risk analysis methods and the related models by the following directions:

I. depending on attraction of probabilistic distributions:
• methods without distributions of probabilities;
• methods taking into account distributions of probabilities.
  II. depending on accounting of probability of realization of each separate value of a variable and carrying out all process of the analysis taking into account distribution of probabilities:
• probabilistic methods;
• sample methods.
  III. depending on methods of finding of resultant indicators on creation of model:
• analytical method;
• imitating method.

Sign of approach of methods I of group is that for each stochastic size only one its value undertakes. The purpose of such "condensation" of risk of an exogenous variable is a receiving a possibility of application of the methods developed for the analysis in definiteness situation without any changes.

Not the separate value of a resultant variable, and distribution of probabilities will be calculation result on the model designed for approach of II. Probabilistic methods assume that construction and calculations for model are performed according to the principles of probability theory whereas in case of sample methods all this becomes by calculations for selections.

Characteristic feature of approach of II is use of methods of modeling of decision making. Here it is possible to allocate target, optimizing and system approaches. The accurate task of the purposes when designing model is peculiar to target approach. Any change of target indicators leads to reconstruction of the model and demands new calculations that is connected with additional costs. Application of this approach most expediently in case of need constantly to make decisions in similar situations with precisely set purposes.

System approach is connected with creation of the model directed only to reflection of reality, but is more whole than not formulated system. As a result of assessment of such model and calculations for it the description of behavior of a real system, but not the optimum strategy of actions is created. Then the system of the purposes is chosen and there is possible decision making by means of expected information on behavior of a system and the made assumptions. Does not lead the changes of the purposes arising in the course of investment design to change of the model and do not demand new calculations.

Approach of III allocates analytical and imitating methods of finding of resultant indicators on the constructed model. The analytical method of obtaining results is performed directly on the basis of values of exogenous variables. To its benefits speed of finding of the decision, belongs to shortcomings - need of adaptation of an objective to an available mathematical apparatus and its relative small "transparency". The imitating method is based on step-by-step finding of value of a resultant indicator due to carrying out repeated experiences with model. Its main benefits - transparency all of calculations, simplicity of perception and assessment of analysis results of projects by all participants of planning process. As one of massive faults of this method it is possible to call essential costs for the calculations connected with the large volume of output information.