Informatics and Applications

2018, Volume 12, Issue 2, pp 50-59

A MODEL OF RISK MANAGEMENT IN GAUSSIAN STOCHASTIC SYSTEMS

A. N. Tyrsin
A. A. Surina

Abstract

A new approach to research of risk of multidimensional stochastic systems is described. It is based on a hypothesis that the risk can be managed by changing probabilistic properties of a component of a multidimensional stochastic system. The case of Gaussian stochastic systems described by random vectors having the multidimensional normal distribution is investigated. Modeling has shown that multidimensionality of a system and relative correlation of components unaccounted in an explicit form, can lead to essential understating of risk factors. Results of calculation of the probability of a dangerous outcome depending on numerical characteristics of a multidimensional Gaussian random variable (a covariance matrix and a vector of mathematical expectations) are given. Approbation of the suggested model is executed by the example of the analysis of the risk of cardiovascular diseases in population. Models of risk management in the form of a minimization problem or achievement of the given level are described. Control variables are the numerical characteristics of a random vector covariance matrix and a vector of mathematical expectations. Approbation of the method of risk management was carried out by means of statistical model operation by the Monte-Carlo method.

[+] References (18)

Gore, A. 1992. Earth in the balance. Forging a new common purpose. London: Earthscan Publications Ltd. 440 p.
Vorob'ev, Yu. L., G. G. Malinetskiy, and N. A. Makhutov. 2000. Upravlenie riskom i ustoychivoe razvitie: chelovecheskoe izmerenie [Management of risk and sustainable development: Human measurement]. Izvestiya vuzov. Pri- kladnaya nelineynaya dinamika [Proceedings of the Uni-versities. Applied Nonlinear Dynamics] 8(6):12-26.
Porfir'ev, B. N. 2006. Snizhenie prirodnykh riskov ekonomicheskogo razvitiya Rossii: rol' gosudarstva [The reduction of natural risks of economic development of Russia: The role of the state]. Aktual'nye problemy grazhdan- skoy zashchity: Mat-ly 11-y Mezhdunar. nauch.-praktich. konf. po problemam zashchity naseleniya i territoriy ot chrezvychaynykh situatsiy [Actual Problems of Civil Protection: 11th Scientific and Practical Conference (In-ternational) on Problems of Protection of the Population and Territories from Emergency Situations Proceedings]. N. Novgorod: Vector-TiS. 44-50. Available at: http://gov.mari.ru/debzn/omgo/46.djvu (accessed August 7, 2017).
Porfir'ev, B. N. 1991. Upravlenie v chrezvychaynykh situatsiyakh. T. 1. Itogi nauki i tekhniki. Problemy bezopasnosti: chrezvychaynye situatsii [Management in emergency situ-ations. Vol. 1. The results of science and technology. Secu-rity concerns: Emergency situations]. Moscow: VINITI. 204 p.
Vishnyakov, Ya. D., and N. N. Radaev 2008. Obshhaya teoriya riskov [Common theory of risks]. 2nd ed. Moscow: Academy. 368 p.
Akimov, V.A., V. V. Lesnykh, and N. N. Radaev. 2004. Riski vprirode, tekhnosfere, obshchestve i ekonomike [Risks in the nature, technosphere, society, and the economy]. Moscow: Business Express. 352 p.
Solozhentsev, E. D. 2006. Stsenarnoe logiko-veroyatnostnoe upravlenie riskom v biznese i tekhnike [Scenario logic and probabilistic management of risk in business and engineering]. 2nded. St. Petersburg: Biznespressa. 560 p.
Ryabinin, I. A. 2000. Nadezhnost' i bezopasnost' strukturno-slozhnykh sistem [Reliability and safety of the structural and composite systems]. St. Petersburg: Polytechnique. 248 p.
Tyrsin, A. N. 2015. O modelirovanii riska v sistemakh kritichnykh infrastruktur [About model operation of risk in the systems of critical infrastructures]. Economic and Technical Aspects of Safety of Civil Engineering Critical Infrastructures Conference (International) Abstracts. Eka-terinburg: Ural Federal University. 205-208. Available at: http://elar.urfu.rU/bitstream/10995/33468/l/safety_ 2015.pdf (accessed August 7, 2017).
Tyrsin, A. N., and A. A. Surina. 2017. Modelirovanie riska v mnogomernykh stokhasticheskikh sistemakh [Modeling of risk in multidimensional stochastic systems]. Vestn. Tomskogo gosudarstvennogo universiteta. Upravlenie, vy- chislitel'naya tekhnika i informatika [Bull. Tomsk State University. Management, Computer Facilities, and Infor-matics] 2(39):65-72.
Gnedenko, B.V. 2005. Kurs teorii veroyatnostey [Course of probability theory]. 8th ed. Moscow: Editorial URSS. 448 p.
Pena, D., and J. Rodriguez. 2003. Descriptive measures of multivariate scatter and linear dependence. J. Multivariate Anal. 85:361-374.
Kir'yanov, B. F, and M. S. Tokmachev. 2009. Matemati- cheskie modeli v zdravookhranenii [Mathematical models in health care]. Veliky Novgorod: NovSU. 279 p.
Tsinker, M.Yu., D.A. Kir'yakov, and M. R. Kamaltdi- nov. 2013. Primenenie kompleksnogo indeksa narusheniya zdorov'ya naseleniya dlya otsenki populyatsionnogo zdo- rov'ya v Permskom krae [The integrated index of health situation of the population to assess population health in the Perm region. Izvestiya Samarskogo nauchnogo tsent- ra RAN [Proceedings of the Samara Scientific Center of RAS] 15(3(6)):1988-1992.
Profilaktika khronicheskikh neinfektsionnykh zabolevaniy Rekomendatsii [Prevention of pre-existing conditions. Recommendations]. Moscow. 128 p. Available at: http://www.webmed.irkutsk.ru/doc/pdf/prevent.pdf (accessed August 7, 2017).
Tyrsin, A. N., O. F. Kalev, D.A. Yashin, and O.V. Lebedeva. 2015. Otsenka sostoyaniya zdorov'ya populyatsii na osnove entropiynogo modelirovaniya [Assessment of health status of a population on the basis of entropy modeling]. Math. Biol. Bioinf. 10(1):206-219. doi: 10.17537/2015.10.206.
Mihaylov, G. A., and A. V. Voytishek. 2006. Chislennoe statisticheskoe modelirovanie. Metody Monte-Karlo [Numerical statistical model operation. Monte-Carlo methods]. Moscow: Akademy. 368 p.
Panteleev, A.V., and T.A. Letova. 2008. Metody optimizatsii v primerakh i zadachakh [Optimization methods in examples and tasks]. 3rd ed. Moscow: Higher School. 544 p.

[+] About this article