To the concept of the ecological risk. Analytical review of the publications

The modern riscs of the oil pollution in the Arctic

The Arctic wildlife area is of particular importance in the light of the global natural and socio-economic changes in the world today. Depletion of energy resources and the increasing availability of the Arctic marine waters are attracting more attention to energy, transport, recreational facilities in the Arctic region of the planet. Simultaneously, the attention to environmental security in the Arctic, which is often put at the forefront and can be an obstacle to the development of the resources of the Arctic shelf. In this context, time-needed development of the methods for assessing the environmental risks from adverse effects of the environment and recommendations to ensure the environmental safety.

In 2011, in the Pechora Sea was established operational and drilling platform in the oil field "Prirazlomnoe". Also operates in the Pechora Sea offshore ice-resistant offloading Varandey with subsea pipeline. Branches laid underwater gas pipeline from the Yamal Peninsula in the Baydaratskaya Bay. A draft of the Shtokman gas condensate field in the Barents Sea. Begins the work on the development of the north-eastern part of Prinovozemelsky shelf in the Kara Sea. Complex climatic conditions of the Arctic shelf create high natural risks to the security of the maritime infrastructure increase the cost of the projects. This adverse weather conditions: low temperatures, the probability of the strong winds, poor visibility, atmospheric icing. Of hydrological conditions should be allocated adverse sea excitement significant fluctuations in sea level due to tides and storm surges, strong currents. The risks caused by ice phenomena: strong ice compression, ice effect on structures in the form of large and giant ice floes and icebergs, ice ridges and hummocks, piles of ice on the shore ice exaration bottom earlier ice formation and many other phenomena.

Disaster in the Gulf of Mexico suggests the possibility of an increased risk of oil pollution, which is especially dangerous in the Arctic based on the availability of ice cover. Modern methodological apparatus of the risk assessment is far from perfect. Some idea of the problems with the state's ecological risk assessment can provide an article published.

The paradigm of the «risc» thinking

Risk estimation theory began its systematic development of 40-ies XX century [1] in connection with the growing needs to ensure security in the aerospace operations and the development of the chemical industry.

This is especially clearly manifested during the development of the nuclear power, which largely contributed to the rapid progress in the field of the risk theory. Large contribution to the theory of the risk introduced British scientist FR Farmer [2], whose work initiated interest in the assessment of the social risks (see, [3]). In the cited paper attention is paid to individual and collective risks, while at the individual risk is the frequency of use of a given individual to damage from exposure to certain hazards. Collective risk - is the ratio of the individual risk to the number of the individuals affected population for a given volume.

Active development of the theory of the risk in the 80sof the last century contributed to new challenges, primarily with the development of the nuclear energy, aerospace studies (program "Apollo" catastrophe "Challenger") and the chemical industry [4]. In this, which has already become a classic, work, risk means, in accordance with [5], a set of scenarios, each of which has a probability (frequency) of the implementation and its consequences. Under numerical characteristics are understood statistics quantities such as, for example, mortality, reduced life expectancy, etc. To calculate the statistics used apparatus of the probability theory, and the procedure of the risk assessment has received the names of the probabilistic risk analysis (Probabilistic Risk Analysis).

Understanding the importance of the problem assessment of the human impact on the environment, coupled with an awareness of the finiteness of natural resources and the progress of the theory of the risk led to the development of the theory and the practice of evaluation of the natural (environmental), and in particular , the environmental risk. The main application of new ideas - the sphere of the political and practical solutions related to the management of natural resources (environmental), and in this sphere involves not only government and business, but also the general public. These problems created a new science - the "natural» sociology (environmental sociology), one of the main concepts which is the risk.

In [6], a comparative characteristics of the different approaches to the assessment of the natural risks in the context of the problems of the nature and political decision-making. In particular, according to the authors, the traditional approach to the natural risk assessment was focussed on the impact of chemical pollutants on human health. Risk assessment methodology was based on four steps: hazard identification, risk assessment of the critical dose, identification of potential objects and methods of influence, and finally integrated risk assessment. With the use of expert treatments are based on statistical estimates of the probabilities of harm to a person by natural or anthropogenic agents is the result of the recommendations for planning / management activities, taking into account a certain degree of uncertainty.

In the following approach to risk assessment was developed in two directions: in the field of social problems in the area of the environmental problems. The authors [6] note the interesting fact that the classification of formaldehyde and DDT to risky drugs held not by the analysis of mortality, disability, or harm to the environment, but as a consequence of the differences and incompatibility of the results of observations and discussion of these effects among experts and key figures based on moral obligations at the level of decision-making. The second direction (environmental risk assessment) was developed in the connection with the extension of a set of objects by incorporating risk into consideration the state of the species diversity of flora and fauna (ecosystems).

Exhaustive in its completeness example risk assessment of marine activities in the Belgian part of the North Sea (BCHSM) (including risks and negative impacts on the environment) can serve as project RAMA [7]. Risk analysis , in particular, involved a detailed list and description of nature waters characteristic of movement routes , geographical distribution of vessels turnover for quantitative analysis of the different types of cargo, accident analysis in the waters , a risk assessment model of maritime accidents (Marine Accident Risk Calculation System, Marcs) , description of the results of the model Marcs, the description of the spatial distribution of biological communities BCHSM analysis of their importance and protected status , determination of levels of sensitivity (vulnerability) of the environmental and the socio-economic parameters, lists of the environmental and the socio-economic parameters of the coastal and marine waters, mapping vulnerabilities coastal and marine areas within the overall scenario and seasonal scenarios, modeling the effects of oil spills, to develop recommendations for the decision-makers and suggestions for the development of the risk assessment of maritime activities.

RAMA project was carried out within two years of the two Belgian partners: consultancy Ecolas NV (Environmental Consultancy Agency) and the Marine Institute of the University of Ghent (Maritime Institute, University of Ghent).

Given that risk assessment techniques in the environmental (environmental risk assessment) still need to be improved, they are not fully applied in the assessment of the environmental impacts (environmental impact assessment, EIA) (at least in Australia [8]). Nevertheless, it is believed that the ERA can be a good tool for the implementation of the paradigm of "green economy" [9].

Currently paradigm "risk thinking" becomes an accepted norm. For example, in the U.S. National Strategy for the Arctic [10] noted that U.S. efforts in the protection of the Arctic environment and conservation of the natural resources of the Arctic should be based on the risk assessments (risk-based) ecosystems, taking into account the possible impact of climate change and other stressors. In Russia, a similar approach has been previously recorded in the Ecological Doctrine [11].

The theory riscs

Developing in the field of engineering sciences and in decision-making with practical application in the insurance and military affairs, financial operations, solving problems of food security and the preservation of health in hazardous production, risk theory has found application in envi- ronmental science and the practical arrangements for the Conservation of Nature (in terms of the formation of policies and legislation). Starting this process put the Agency's U.S. Environmental Protection Agency (US Environmental Protection Agency, EPA). As a result, there was a set trend in the theory of the risk, based on different principles and methodologies. Formed the basic concepts of the natural hazards assessment (ERA), human health risk assessment (Human Health Risk Assessment) and the environmental risk assessment (Ecological Risk Assessment).

At time of writing [1, 12], according to the authors, there was no unified theory of risk and consistent terminology, including the definition of risk. In particular, it explains the ambiguity of the notion of risk in everyday life (and linguistic) terms. It should be noted that noted in [1] position with a unified theory of risk persists nowadays .

Most definitions of the risk include three common elements: [1]

• a)    The possibility of the adverse consequences (injury, damage, loss).

• b)    The likelihood that adverse effects will happen (as a measure of the uncertainty of the fact of an event, the timing and magnitude of impacts).

• c)    Functional relationship between the probability of the event and the magnitude of adverse effects.

The modern trend bias methodological basis of the orientation of the danger to a focus on risk has the effect of desire for clear separation of concepts danger of adverse effects, on the one hand, and risk, as such, on the other. At the same time more attention is paid to the system of relationships between these components.

With reference to the problems associated with the environment, the modern definition of risk require the presence of such localized components, the danger, the impact (including the impact of the object and the method of exposure), adverse effect, conjugation above components, and finally uncertainty. The details of these concepts are described [1].

The same authors formulate environmental risk as a measure that combines the probability (frequency) of a hazard and the magnitude of adverse effects (harm) to human health or the natural elements or artificial environment. The risk increases if increases the likelihood or magnitude of the harm or both together. Adverse effects include damage, illness, damage to natural resources, species reduction, property damage, economic losses, etc.

In [13] provides a detailed overview of existing approaches to the concept of risk assessment and application. In particular, to the areas where risks are used, the author considers the financial sector and the engineering, management, social services (including medicine) and, in particular detail, and military affairs. In each field, different approaches to the numerical expression of risk: currency units, size of territory, the degree possible disease / death and destruction facilities, the level of public / political support, etc. The main procedures related to risk analysis includes risk assessment, risk management, the interaction of risk and decision making. "Technological" risk analysis procedures are well developed and include techniques such as flow-profit analysis (cost-benefit analysis), analysis of the tree (graph) failure (fault tree analysis), the establishment of the strategic objectives (strategic objectives at risk (SOAR)) and other key issues, risk assessment author calls complexity (complexity), uncertainty (uncertainty) and ambiguity (ambiguity).

An example of the complexity of the problem of risk assessment may serve as a fire risk assessment. In the assessment of the risks of fires authors of [14] include two types of risk: the risk of fire and the risk of negative consequences of fire to ecosystems. Fire risk is estimated as the risk of fire and the spatial distribution of fire, taking into account the intensity and duration of the fire, and ecosystem risk assessment includes the effects of fire for flora and fauna, as well as the impact on the soil, which may have a longer duration of time. The toolkit is designed to assess the risk in the assumption that the vegetation and climatic parameters are relatively stable, and taking into account possible changes in time. The risk assessment is performed using the predictive models of three types: biophysical model predicting the risk of fire depending on the type of vegetation, the statistical models and life cycle of fire. From the viewpoint of ensuring Hydro should be noted that the first type of model uses the climatic information, and the third type uses a spatial distribution and topography of the wind.

In probabilistic models of fire risk, risk means (1) the probability of occurrence of fire, (2) the conditional probability of a severe fire on the condition that the fire occurred, and (3) the unconditional probability of a large fire.

To scale systemic risk (systemic risks), due to events that have uncontrolled large-scale consequences, in addition to the risks of natural disasters (earthquakes, tsunamis, hurricanes, volcanic eruptions, etc.) or the risks of industrial accidents engineering systems (disconnection of electrical networks, nuclear accidents, etc.) by [15] also considers the risks and major social problems. These include the problems of hunger, lack of resources, war, the problem of possible conflicts due to climate change, pandemics, financial crises, etc. To analyze the risks involved in such research methods chaotic structures, self-organization of complex systems, the methods of nonequilibrium thermodynamics, bifurcation theory, etc. (see for example [16]).

Modern view of the sources of the risk in the Arctic is presented [17]. Among the risk factors, we include a group of the natural factors (geographical isolation, storms, icebergs, the effect of low temperatures on the mechanisms, polar night, environmental vulnerability, risk of pollution, high responsibility for the impact on the environment, the risk of the emissions from drilling problems offshore operations expertise), group of the economic factors (lack of the development of maritime infrastructure, high levels of investment, the complexity of logistics, potential delays to ships / units, the need for the unique technologies, non-diversified equipment suppliers) and a group of socio-political factors (political aspects, reputation, regulation, tax policy variability, "resource" nationalism, terrorist threats, interactions with indigenous people).

The concept of the risc: a dual approach

Virtually all authors of publications devoted to the problem of risk, note the absence of a rigorous and generally accepted definition of the risk. The spectrum is very broad set of definitions from general methodological formulations to rigorous mathematical concepts. An example of the qualitative determination of risk can serve as a form of the words in the textbook [18] devoted to the theory of the economic risks in the management of the organizations, where the category of "risk" is defined as "a danger of the potentially possible, probable loss of resources or revenue shortfall compared with one that is rated for rational use of resources in the form of entrepreneurial activity. In other words, the risk - is the threat that the entrepreneur will suffer losses in the form of additional costs or receive income lower than those for which he had hoped".

Another example can be found in [19]: "... the canonical definition of the risk modern science does not give. About two dozen known definitions are reduced to partially uncertain possibility of the future losses, the value of which depends largely on some of our current actions. We define risk as a property of the scenarios, which consciously or unconsciously active system is estimated at ranging options for the future in terms of their preference for you".

In the tutorial [20] under the risk is taken to mean "the probability (threat) loss of the person or organization of their resources, revenue, or the appearance of additional costs resulting from the implementation of certain operating and financial policies". Textbook author introduces two important types of the risk: "Risk is divided into dynamic and static. Dynamic risk associated with unforeseen changes in the cost of capital due to management decisions, as well as market or political circumstances. Such changes may result in losses as well as additional income. Static risk due to the possibility of loss of the physical assets due to damage to property and loss of income due to disability organizations". In other words, the dynamic risk due to initiative activity, while static risk is determined by the external circumstances.

Analysis of the literature allows two main approaches to the concept of the risk:

• a)    Risk - is the expected damage (usually in monetary terms) with the measure of the uncertainty of its achievements.

• b)    Risk - is a dimensionless measure of the uncertainty of the adverse events with a given damage / level of damage.

Apparently, the first approach is due to the use of the notion of risk in finance [21, 22, 23] and especially the insurance business, in which the theory of risk is most developed, which led to the isolation of mathematical methods of risk assessment in the special branch of mathematics -the so-called actuarial mathematics (see, eg, [24, 25]). The second approach is likely, with the expansion of the application of the notion of the risk in the direction of the decision-making processes to ensure the safety of the operations.

The fundamental difference between the approaches can be partly explained by the fact that, as the authors of [26], in English, the word "risk" has two meanings: there is an adverse event and the probability (possibility) of this event. The relationship of these approaches is obvious: with the totality of the uncertainties of the adverse events with the specified damage to an exhaustive set of different damages can estimate the expected average (maximum, minimum, most likely, etc.) damage and get an idea of the probability distribution of damage. Thus, under the damage can be understood and the broader concept of the harm in their respective units.

The author gives examples of 17 different definitions proposed in the period from 1901 to 2009., 14 of them formulate risk as the probability (likelihood) of an undesirable effect (general or specified) and two definitions contain the term "combination" probability of an event and its magnitude, one definition is given as the average damage and, finally, the definition of ISO 2009, which is at risk understands the impact of uncertainty on objectives. In the same paper published a table of mathematical expressions to risk used by specialists from various disciplines (engineering, ecology, toxicology, fisheries, biosecurity and decision theory). In most cases, the expression for the risk are of a general nature, does not allow to perform calculations, and explicitly in any number of arguments in the expression does not include the meteorological parameters.

Demonstration (in the sense of looseness) definition of the risk is given in [29] : the risk -this is a conceptual term used to realize the objects of forces or circumstances that may pose a threat (danger ) to persons or property. Description of the risk, as normally done in the terms of the plausibility of harm or damage from hazards and usually involves the identification of possible harm or damage (risk objects can be, for example, human health or the biosystem, property, quality of life, economic activity), a hazard that can cause to harm or damage, and perceptions of the likelihood of this event.

Another example of "vague" definition of the risk is the work [30]. At risk is defined here as characteristic of the system, which are known to the likelihood that certain states or outcomes occurred or may occur. Risk – is a combination of the probability of the event and the corresponding consequences. Decisions made based on the risk related to decisions under uncertainty.

At the same time, the basic document of the World Health Organization is uniquely at risk is the probability of adverse effects on the body, (eco) system, the population (or part of the population), produced by an external action in certain circumstances [31]. When this effect is considered to be a change of state or object dynamics effects.

Vagueness in the definition of risk traced to the last time. For example, the guidelines prepared by the University of Cranfield (Cranfield University) [32], at risk refer to the potential consequences of hazards in conjunction with their probabilities (likelihood). It is noteworthy that in many publications either did not give a definition of risk , or the definition is of a qualitative nature (including, for example, the word "combination", " integration", etc. [33]), with a very detailed description of the risk assessment procedure as multielement process.

To date, the methodology of the risk analysis and management in procedural terms is sufficiently well developed. Common approaches are detailed in the international standards [34, 35], and the versatility of the presentation allows the use of the methodology developed in almost all areas of activity. Such versatility is due to the homogeneity analysis and prediction problems arising in the risk analysis.

According to the approach of the International Standards Organization (the International Organization for Standardization, ISO), the risk - is "the effect of uncertainty on objectives" [36, 37]. Detailed description of the new standard adopted instead of the standard [38], can be found in [39]. In the same paper stresses that the new definition of the risk improves the former restricting the concept of the risk "combination" of the influence and uncertainty.

In [40] a comparative analysis of the international standard ISO 31000:2009 standard and the Committee of Sponsoring Organizations of the Treadway Commission (The Commit-tee of Sponsoring Organizations of the Treadway Commission, COSO, USA). In the latter, risk means the possibility of an event that may have a negative impact on the achievement of objectives. Characteristically, the COSO definition explicitly formulates risk as a measure of uncertainty, however, limits the scope of the consequences only goals. Identifying risks to ISO 31000:2009 as " the effect of the uncertainty on objectives" prioritizes Impact Assessment under uncertainty.

A detailed analysis of the various approaches to the problem of the risk management as an example of the standard [41], risk management research at the Institute (UK, Institute of Risk

Management), "Orange Book" of the Ministry of Economy and Finance UK (HM Treasury) and the International Association "Institute of Internal Auditors" (Institute of Internal Auditors) is given in [42]. In general, it can be noted that the duality in the definition of еру risk persists.

Determined research

Although attributiveness uncertainty in estimates of the risk is well recognized, the deterministic approach remains relevant. The article [43] describes a deterministic approach to the concept of the ecological risk ( risk ratio (riskquotient, RQ) as the one introduced for evaluating the concentration of the substance (Predicted Environmental Concentration, PEC) to the evaluation of a safe concentration (Predicted No-Effect Concentration, PNEC). PEC size is determined based on the impact and the magnitude PNEC estimated by analyzing the effect produced. Case when RQ is greater than one means that bringing the substance can lead to harmful consequences.

A similar approach was applied to the multiplicative pollution sources when adapted to the seasonal characteristics and types of the natural disasters were proposed in [44]. In Soviet literature the same approach given in the textbook [45].

The authors of a major European project to develop ARAMIS scenario approach to (technological) risks (the cast includes 14 scientific organizations from seven countries: Denmark, Spain, Italy, Poland, Slovenia and the Czech Republic) use the concept of a risk index, which is defined as a measure (quantitative or qualitative), a combination of factors that pose a threat to (technical) system [46]. An important characteristic of the risk, according to the authors [46], is a severity index risk (the risk severity index), which is defined as the sum of the probability of hazards (dangerous phenomen) and specific for each factor indices seriousness of the risk. Summation is over the number of hazards. Here it is assumed that in the case of the critical events (critical event) may occur several hazards, with varying degrees of negative effects (specific indices seriousness of the risk). Specific indexes are measured on a scale from 0 to 100 for four levels of effect (slight, reversible, irreversible and catastrophic).

The overall index is calculated by summing the severity of risk by number of critical events products of probabilities (frequencies) of critical events on the seriousness of the risk associated indexes and normalized in the range from 0 to 1000. Next introduce four levels of the overall index seriousness of the risk: the values within the more than 750 risk of extremely high, from 750 to 300 - high risk, from 300 to 50 - the average risk for the other values - low. Calculating risk severity index as a function of the distance between the source of danger and risk evaluation point, you can build a map of zoning (in the general case in three-dimensional space, and even taking into account the time) on the degree of risk of danger that is the methodological basis for zoning. For more details see [47].

Risc as a combination of damage and probability

As already noted, the concept of risk as expected damage (often in conjunction with the probability of damage) is very common. In most studies published up to mid- first decade of the XXI century. , At risk is defined as "a combination of (a combination of) the probability of an event and its consequences" [48, 49]. The authors of [5], risk means a set of the scenarios, each of which is characterized by its probability of implementation and its consequences. The review [50] devoted to the analysis of the publications period 1976-1981. Concerning the problem of the risk assessment in the nuclear power industry, the following definitions of the risk:

• a)    The risk of the expected effects.

• b)    As the probability of the risk coupled with the effects.

• c)    Risk as the probability of disaster.

• d)    Risk as a general concept that reflects the consequences of the measure or harm.

Examples of this approach are the work of [51, 52], etc. The same approach to the definition of risk (including environmental risk) is given in the textbook [53]. Authors benefit under the negative consequences understands damage, expressed in monetary units. In [54] we noted that the usual interpretation of the notion of the risk as a combination of hazard and vulnerability is not a mathematical operation, but is intended to fixation probability of an adverse event due to the expected outcome. Noting that the most important role in the risk assessment is the notion of uncertainty, the authors analyze the approaches based on probability theory, fuzzy logic, and combinations thereof, giving preference to the hybrid approach. In a tutorial [55] (see also the second edition [25]) in the informal interpretation of the risk is "a set of values possible damage to some stochastic situation and its probability".

In [56, 57] technogenic risk is considered as the expectation of consequences (damage) from the accomplishments of the initiating events, the probability of the event and the value of the damage taken as random variables (independent or dependent).

Fundamental work [58], three editions, contain the details of the risk analysis process with examples of risk assessments, feasibility of the projects, a variety of the financial risks, risks in the insurance business, as well as risks of the violation of the microbiological safety of food and animal imports. Basic concept of risk – is the expected damage. Furthermore, the author introduces the concept of "rigidity” (severity) of risk as the sum of the probabilities ranked adverse events and ranked variables damage. It should be noted that to date have been developed and successfully implemented software for analyzing risks. In particular, the software company ModelRisk based on the results.

The authors of [59] the actual risk is considered the product of probability of an adverse event (accident) the degree of adverse, meaning by the latter product hazard index object vulnerability risk, calculated in terms of the conventional integer (0 to 10). The objects of risk are protected natural areas (national parks, basic farmland, wetlands, areas with a given population density, raw land, etc.).

Following [46], the authors of [59] introduced the concept of natural risk zones (environmental risk field, ERF) for spatially distributed groups of territories subject to risks of various origins as an integrated result of cumulative impacts. ERF allocation suggests that, although some parts may contain a variety of the natural ingredients, "risky conditions" are the same for all parts. For each of the ERF can be determined intensity of the risk (risk intensity) as a spatial effect of the source of risk regardless of the risk objects. Risk intensity is calculated by summing the products of the probabilities of various pollution emissions intensities and private risk (for this type of pollution.) The summation is over the number of cases of pollution emissions. Private risk intensity is determined by the authors [59] as the ratio of the concentration of a pollutant after the release and distribution of the maximum permitted concentration and is also called the hazard index (environmental hazard index).

These structures are the basis of zoning of space on the degree of risk. The degree of risk posed by a sudden release of the pollutants is influenced by two factors: the intensity of the ERF (as a potential exposure to hazards) and the vulnerability of the environment (the vulnerable targets, the higher the risk of adverse effects). When zoning are three zones: the acceptable risk (high resistance to impacts), high-risk area (excess risk situations requiring proof of industrial development and protection measures) and an area in need of reducing the risk (the risks are high and intervention is required to reduce the risks or by reducing the sources of danger, either by controlling the ratio of the hazards and risk objects).

The problem of uncertainty

Understanding the leading role of uncertainty analysis and risk assessment, including environmental risk, contributed to the development of the statistical approach, the basic methods which are probabilistic (frequency) analysis and Bayesian approach [60]. In [61] provides an overview of the development of probabilistic analysis in risk assessment. According to [62], the concept of risk refers to the effect of uncertainty on the achievement of objectives. Risk describes the probability of an event and its "contribution" on a par with the ability to impact on the achieve- ment of the objectives of a certain structure (organization). As you can see, this definition is consistent with the definition of an international standard [41]. Principally unavoidable uncertainties in the process of the risk assessment excludes the possibility of making the perfect solution, but leaves the chance to select the "best" solution [63].

A Bayesian approach to risk assessment is a means of better understanding of the impact of uncertainty on the risk assessment, to study the mutual uncertainties of different nature, and is also used to justify the inclusion in the calculation of the amount of risk of subjective measures of confidence and expertise and verification risk assessment models [64, 65]. Proposals for the application interval estimation (in a probabilistic interpretation) can be found [66].

Risc as the probability of the expected damage (harm)

Non formalised terms "combination", "combination" (see [67]), "taking into account" [68] reflect the complexity of the risk assessment, a decision which in specific cases suggests that a comprehensive analysis of the sources of danger to an activity from both the external environment, and inducible activity itself, followed by qualitative analysis.

Thus, according to the federal law "On technical regulation" [68], "risk - the probability of harm to the life or health of people, property, natural or legal persons, state or municipal property, the environment, health or life of animals and plants according to the severity of that harm . "

In the book [69], the following discussion of the concepts of the risk and vulnerability of therisk: "It seems that the category of the "risk" is derived not only from the concept of "danger" (which has been emphasized by many researchers), but the concept of "vulnerability". It characterizes the loss of the object (subject) stability (security) to the exertion of the adverse effects "and defines the probability of danger as a formula of total probability (though «in the implementation of some set of events ", while the combination of these events has not been disclosed), but under risk, after all, meant the traditional notion of average damage".

But already in the law "On Environmental Protection" [70] for the definition of the environmental risk given no vague terms: "Environmental risk – is the probability of an event that has adverse effects on the environment and the negative impact caused by the economic and other activities, emergencies and natural manmade".

One rigorous approach to the "combination" of damages and uncertainties can serve a quote from [55]: "...theoretical probabilistic analogue of damage, obviously, is the notion of a random variable. Same set of values of a random variable and their probabilities in the theory of probability given by the distribution of the random variable. Thus, under the risk would like to understand the random variable. However, if the risks are identified with random variables defined on different probability spaces, the problem of comparing such risks is fundamentally unsolvable and even meaningless, since the corresponding random variables as a function of elementary outcomes depend on the arguments that have different meanings. Therefore, in such situations have to identify the risks of distribution functions". In the work cited object of study is the outcome of the random variable insurance fund or a cash balance of the insurance company to some fixed set of insurance contracts.

Mathematical modeling study of the financial risks as a functional on the set of the distributions with certain properties developed in [70]. In this paper, the measurement of the risk is understood as a quantitative description of the preferences on the set of probability distributions.

Concise , but an exhaustive definition of the risk given in the lectures [71], where the risk is any distribution from the set of probability distributions on a measurable set of results ( ie, the set of results with the corresponding σ- algebra) . In a rigorous formulation of the problem in [55, 25] at risk (more precisely, under individual risk) refers to the distribution of a random variable ( in the dynamic case - random process) of the outcome of the insurance fund or a cash balance of the insurance company on some fixed insurance portfolio.

Because not all damage can be given in value (and sometimes even in numerical) terms (especially environmental safety, health and social problems), with an a priori analysis of the possible negative consequences of the emphasis is on the assessment of the uncertainty of the hazardous events. For example, in [72], risk means uncertainty in the occurrence of the consequences that may affect decision-making. Some of these effects may include opportunities (loss) income, damage to health or other effects affecting the welfare, ie uncertainty that "matters".

According to [73] the risk criteria are expressed by the probabilistic nature and are determined by the probability (or frequency) of the threats to human society and the state and the amount of damage caused by this realization. In some cases, under the criteria of risk only understand the likelihood or frequency of adverse, hazardous or catastrophic events.

A glossary (which is typical for this type of the documents) with a breakdown of all the special terms. In particular, the concept of the risk is understood in four ways: 1) the risk includes consideration of the possibility of an adverse outcome, the frequency with which one or more adverse events occur, including the seriousness of the consequences, 2) at risk refers to the ability of the unwanted, negative consequences to human life, health, property or the environment, and 3) the likelihood of adverse effects as a result of exposure to one or more environmental factors, and 4) the answers to the questions: what can go wrong, as far as reasonably and what are the conse- quences.