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Hybrid Logical and Probabilistic Risk Models

Nobel Prize Laureates James Buchanan and James Heckman in their works (Buchanan, 1985), (Heckman and Leamer, 2001) have considered connections between economics and politics in evolution of State with use of game theory and statistical data analysis.

As a further growth of their ideas we are offering the new approach for analysis and management of economic safety of socioeconomic systems (SES) on basis of Top-Economics (Solozhentsev, 2015a and 2015b). We are considering connections between economics, State, politics, business, science and society. Initiating events, depending from State, business, science and society are taking into account in LP risk model and signal events are changes in economics, politics, rights, innovations, natural disasters and wars, situation at world market, etc., for correction of probabilities of initiating events (IEs) in LP model of SES's risk.

There is the following hierarchy of socio-economic systems and problems: large SES (country), socio-economic problems in country, SES of State. In present work we are considering approbated LP risk models for economic safety management in SESs of State, for example, Russia. These systems are real and understandable for population. With help of LP models it is possible to estimate and analyze the SES's invalidity risk and allocate resources to manage invalidity.

In SES, the leading model is LP model of risk of failure but, for whole analysis, LP risk models of invalidity, conceptual LP models for forecast and indicative LP models of system's danger are applied.

SES - 1 group contains SESs which are most important for State aimed on reduction of losses and increasing of profits (Solozhentsev, 2015a and 2015b):

  1. Management of innovation system of the country,
  2. Counteraction to bribes and corruption,
  3. Counteraction to narcotization,
  4. Management of quality of systems and production under WTO requirements,
  5. Management of capital reservation in banks according to Basel III,
  6. Monitoring and crediting process management in banks.

SES - 2 group includes complex SESs for State and regions depending on several Ministries, departments and legislative authorities, for example: LP risk model of birth rate in the country, LP risk model of education system failure, LP risk model of failure of informatization, etc.

SES - 3 group includes local SESs for companies and enterprises, those success depends on, mainly, their desires and possibilities, for example: LP management of risk and efficiency of restaurant ("Prestizh"); LP risk models for management of SJSC company "Tranzas", LP risk models for company "Logvin Road + Rail Rus".

Note, in micro- and macroeconomics there is no economic safety management of socio-economic systems in groups SES-1, SES-2, SES-3.

New kinds of events-propositions in economics. New kinds of boolean events-propositions with probabilities of true are entered. The set of propositions forms complex derivative event. In fact, standards, instructions, demands and forecasts are formulated as propositions which have probabilities of true, success or danger. Probabilities of success/failure, stability/danger, validity/invalidity are used for events in management of SES's economic safety under risk criterion. Contributions of outstanding scientists G. Boole, P. Poretsky, S. Bernshtein, А. Kolmogorov and V. Glivenko in LP-calculus for estimation of reliability of technical systems were estimated by I. Ryabinin (Ryabinin, 2007). In evolution of LP method we are entering new kinds of events-propositions: failure of subjects, signal events, events of invalidity, conceptual events, indicative events (Solozhentsev, 2015a and 2015b):

  1. Events-propositions about failure of complex problem decision by subjects: State, business, banks, scientists, public opinion.
  2. Signal events-propositions in economics, politics, rights and laws, innovations, changes at world market are used for correction of probabilities of IEs.
  3. Events-propositions about invalidity are propositions about deviations of parameters from given values. Parameters are normative and within [0, 1]. Event-proposition about invalidity has a risk, which is equal to parameter.
  4. Conceptual events-propositions forecast system's evolution. Probabilities of true of events-propositions are estimated by expert information.
  5. Indicative events-propositions are considered as invalid events. Their measure of danger is deviation of parameter from given values.
  6. Events-propositions about latency. Probabilities of events-propositions are estimated by results of public opinion polls and information from social networks.

New kinds of LP risk models. New kinds of LP risk models for SESs are entered on basis of events-propositions (Solozhentsev, 2015a and 2015b):

  1. Hybrid LP risk models of socio-economic problem decision. These models are constructed on basis of risk scenario for subjects, which are taking part in problem's decision, and risk scenario for objects-tasks, which are the sense of the problem;
  2. LP-models of invalidity are constructed by invalid events;
  3. Conceptual LP models forecast risk of state or evolution of the system. They are constructed on basis of descriptions, produced by specialists, who are understanding the sense of the problem;
  4. Indicative LP models of system's danger are constructed by invalid indicative parameters.

These new kinds of LP risk models can be used for comprehensive analysis and economic safety management for SES-1, SES-2 and SES-3.

Concepts and principles in management of socio-economic safety of SES:

  1. Principle of management by risk criterion with possible loss estimation;
  2. Social justice concept, realized by Nobel dynasty, is the following: the main part of profit are spent for workers and staff: reasonable salary, domestic buildings, kindergartens and schools, free medical service, increase of professional skills, development of science and innovations;
  3. Concept by Chinese administration (Li Keqiang): technological innovations and innovations in management (including innovations in public administration) are equal;
  4. Principle of management of system's development as complex object control with movement on given trajectory and correction in case of deviation;
  5. Principle of management by signal events with correction of probabilities of initiating events (IEs) in SES'LP risk model.

New mathematics in LP risk models. Following new mathematical methods and algorithms are used in Top-Economics:

  1. Concept of "invalidity" in economics by analogy with "failure" in reliability in engineering having many values.
  2. New Boolean events-propositions in economics: failure events of subjects (The State, business, scientists, public opinion); signal events (in economics, politics, rights, innovations, natural disasters and changes on world market); events of invalidity of systems; conceptual events-propositions of risk forecast; indicative events-propositions of system's danger; events-propositions about latency of public interrogate and information from social networks; incompatible events.
  3. Logical and probabilistic calculus.
  4. New LP risk models with events-propositions: hybrid LP risk models of failure in SES's management; LP models of system's invalidity, conceptual LP models of forecast of system's state; indicative LP models of system's danger.
  5. Summarized randomized indexes method for synthesis of probabilities of events.
  6. Methods of construction, analysis and management of SES's risk.
  7. Method of non-linear identification for tasks with large number of real estimated parameters (about 100) and integer optimization criterion.
  8. Proof of impossibility to form identical learning and testing samples in tasks of classification of objects, which are described by parameters with grades.
  9. Algorithm of exception of incorrect and outdated data in tasks of classification of objects.
  10. Algorithm of management of enterprises by contributions of casual events in "tails" of efficiency parameter's distribution.
  11. Algorithm of replacement of LP risk model in task of classification after the forming and analysis of signal parts of objects.
  12. Algorithm of transition from LP model of efficiency to LP model of forecast of risk in space of states.
  13. Bayes' formula in case of limited information.
  14. Special software Expa and Arbiter for calculations and practical works in training course "Top-Economics".
  15. Transformation of any database (DB) in knowledge base (KB) as a system of logical equations for risk tasks.
  16. Interaction of LP risk models of SES with environment by means of signal events-propositions.
  17. Connection of LP risk models of various SESs by means of repeated IEs.

Special mathematics in technology of socio-economic safety management and bases of LP calculus should be studied by students and specialists.


  1. Buchanan, J. (1985) Liberty, Market and State, Wheatsheaf, Brighton.
  2. Heckman, J. J. and Leamer, E.E. (2001) Handbook of Econometrics, Vol. 5, North Holland, Amsterdam, London. 2001.
  3. Solozhentsev, E. D. (2015a) Top-ekonomika. Upravlenie ekonomicheskoy bezopasnostiu [Top-economics. Economic Safety Management]. SPb.: GUAP, 2015. 256 p. (In Russian.).),
  4. Solozhentsev, E. D. (2015b) Nevalidnost' i sobytija-vyskazyvanija v logiko-verojatnostnyh modeljah dlja upravlenija riskom v social'no-jekonomicheskih sistemah [Invalidity and Events-Propositions in Logical and Probabilistic Models for Risk Management in Socio-Economic Systems] // Problemy analiza riska. 2015. № 6. pp. 30-43. (In Russian.)
  5. Ryabinin, I. A. (2007) Nadezhnost' i bezopasnost' strukturno-slozhnyh sistem (2-e izd.) [Reliability and safety of structural complex systems (second edition)]. SPb.: Izd-vo S.-Peterb. un-ta. 2007. 276 p. (In Russian).

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