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On measuring and profiling catastrophic risks

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Cybernetics and Systems Analysis Aims and scope

Abstract

An approach to decision-making under catastrophic risks based on risk profiling is proposed. The approach assumes, for some selected catastrophic scenarios, to simulate their consequences (damage) as functions of control parameters and to impose expert constraints on acceptable levels of relative losses in such scenarios. The approach is illustrated by a number of one-stage decision-making problems reduced to mixed linear-programming problems.

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References

  1. V. I. Norkin, “On modeling spatial, temporal and magnitude aspects in insuring cataclysmic events,” in: Proc. Sec. Intern. School on Actuar. Financ. Math., Kyiv, Ukraine, 8–12 June, 1999, Theory of Stochastic Processes (Kiev), No. 12, 98–110 (1999).

  2. Yu. M. Ermoliev, T. Yu. Ermolieva, G. J. MacDonald, and V. I. Norkin, “Optimization of catastrophic risk portfolios,” in: M. Bonilla et al. (eds.), Papers and Proc. 24th Meeting Euro Working Group on Financial Modeling, Univ. de Valencia (Spain) (1999), pp. 251–269.

    Google Scholar 

  3. Yu. M. Ermoliev, T. Yu. Ermolieva, G. J. MacDonald, and V. I. Norkin, “Stochastic optimization of insurance portfolios for managing exposure to catastrophic risks,” Ann. Oper. Res., 99, 207–225 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  4. Yu. M. Ermoliev, T. Yu. Ermolieva, G. J. MacDonald, A. Amendola, and V. I. Norkin, “A system approach to management of catastrophic risks,” Eur. J. Oper. Res., 122, 452–460 (2000).

    Article  MATH  Google Scholar 

  5. Yu. M. Ermol’ev, T. Yu. Ermol’eva, G. McDonald, and V. I. Norkin, “Problems on insurance of catastrophic risks,” Cybern. Syst. Anal., Vol. 37, No. 2, 220–234 (2001).

    Article  MATH  Google Scholar 

  6. T. Ermolieva and Y. Ermoliev, “Catastrophic risk management: flood and seismic risks case studies,” in: S. W. Wallace and W. T. Ziemba (eds.), Applications of Stochastic Programming, MPS-SIAM, Philadelphia (2005), pp. 425–444.

    Google Scholar 

  7. V. S. Mikhalevich, P. S. Knopov, and A. N. Golodnikov, “Mathematical models and methods of risk assessment in ecologically hazardous industries,” Cybern. Syst. Anal., Vol. 30, No. 2, 259–273 (1994).

    Article  MATH  Google Scholar 

  8. P. S. Knopov and T. P. Maryanovich, “On some actual problems of estimating risk in complex systems under insufficient information,” Cybern. Syst. Anal., Vol. 39, No. 4, 576–585 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  9. I. V. Sergienko, V. M. Yanenko, and K. L. Atoev, “Conceptual framework for managing the risk of ecological, technogenic, and sociogenic disasters,” Cybern. Syst. Anal., Vol. 33, No. 2, 203–219 (1997).

    MathSciNet  Google Scholar 

  10. N. Yu. Kuznetsov and K. V. Mikhalevich, “Reliability analysis of systems described by fault trees with efficiency,” Cybern. Syst. Anal., Vol. 39, No. 5, 746–752 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  11. R. T. Rockafellar and S. Uryasev, “Conditional value-at-risk for general loss distribution,” J. Bank. Finance, 26, 1443–1471 (2002).

    Article  Google Scholar 

  12. V. S. Kirilyuk, “The class of polyhedral coherent risk measures,” Cybern. Syst. Anal., Vol. 40, No. 4, 599–609 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  13. G. Ch. Pflug, “Risk-reshaping contracts and stochastic optimization,” in: IIASA Working Paper WP-96-142, Laxenburg (Austria), Intern. Inst. for Appl. Systems Analysis (1996).

    Google Scholar 

  14. R. E. Beard, T. Pentikainen, and E. Pesonen, Risk Theory. The Stochastic Basis of Insurance, 3rd ed., Chapman and Hall, London, New York (1984).

    MATH  Google Scholar 

  15. M. M. Leonenko, Yu. S. Mishura, Ya. M. Parkhomenko, and M. J. Yadrenko, Theoretic-Probability and Statistical Methods in Econometrics and Finance Mathematics [in Ukrainian], Informtekhnika, Kyiv (1995).

    Google Scholar 

  16. S. Asmussen, Ruin Probabilities, World Scientific, Singapore (2000).

    Google Scholar 

  17. A. N. Nakonechnyi, “Monte Carlo estimate of the probability of ruin in a compound Poison model of risk theory,” Cybern. Syst. Anal., Vol. 31, No. 6, 921–923 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  18. B. V. Norkin, “Method of successive approximations used to solve integral equations of actuarial mathematics,” Author’s Abstracts of PhD Thesis, V. M. Glushkov Inst. of Cybernetics, Kyiv (2006).

    Google Scholar 

  19. A. N. Nakonechnyi, “Optimization of risk processes,” Cybern. Syst. Anal., Vol. 32, No. 5, 641–646 (1996).

    Article  MATH  MathSciNet  Google Scholar 

  20. G. I. Lyubchenko and A. N. Nakonechnyi, “Optimization methods for compound Poison risk processes,” Cybern. Syst. Anal., Vol. 34, No. 2, 230–237 (1998).

    MATH  MathSciNet  Google Scholar 

  21. HEC-FDA Flood Damage Reduction Analysis (User’s manual), US Army Corps of Engineers, Hydrological Engineering Center, version 1.0, Jan. 1998, Approved for Public Release, CPD-72.

  22. Yu. M. Ermol’ev, Methods of Stochastic Programming [in Russian], Nauka, Moscow (1976).

    MATH  Google Scholar 

  23. D. B. Yudin, Problems and Methods of Stochastic Programming [in Russian], Sov. Radio, Moscow (1979).

    MATH  Google Scholar 

  24. A. Ruszczynski and A. Shapiro (eds.), Stochastic Programming, Handbooks in OR and MS, Vol. 10, North-Holland Publ. Co., Amsterdam (2003).

    Google Scholar 

  25. D. Dentcheva and A. Ruszczynski, “Optimization with stochastic dominance constraints,” SIAM J. Optim., 14, 548–566 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  26. H. M. Markowitz, Mean-Variance Analysis in Portfolio Choice and Capital Markets, Blackwell, Oxford (1987).

    MATH  Google Scholar 

  27. W. Ogryczak and A. Ruszczynski, “On consistency of stochastic dominance and mean-semideviation models,” Math. Program., 89, 217–232 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  28. P. Artzner, F. Delbaen, J.-M. Eber, and D. Heath, “Coherent measures of risks,” Math. Finance, 9, 203–227 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  29. A. Ruszczynski and A. Shapiro, “Optimization of risk measures,” e-print available at http://econwpa.wustl.edu:80/eps/ri/papers/0407/0407002.pdf, 24 July (2004).

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Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    V. I. Norkin

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  1. V. I. Norkin
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Additional information

The study was sponsored by the Ukrainian Center of Science and Technology, Project G3127.

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Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 80–94, November–December 2006.

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Norkin, V.I. On measuring and profiling catastrophic risks. Cybern Syst Anal 42, 839–850 (2006). https://doi.org/10.1007/s10559-006-0124-1

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  • DOI: https://doi.org/10.1007/s10559-006-0124-1

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