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Self-insurance of investor under repeating catastrophic risks

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Abstract

A decision-making problem of investment into a profitable object in a catastrophic risk area is considered. By a catastrophic risk is meant the probability of severe yet unlikely losses. As a risk hedging mechanism, an insurance fund is considered that is replenished by a part of profit and is used for object renewal. It is shown that methods of insurance mathematics can be used to assess the risk to lose the object. For the plant loss probability as a function of the insurance reserve, integral equations are derived. They can be solved by successive approximations.

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References

  1. Yu. M. Ermol’yev, T. Yu. Ermol’yeva, G. McDonald, and V. I. Norkin, “Problems of insurances of catastrophic risks,” Cybern. Syst. Analysis, 37, No. 2, 220–234 (2001).

    Article  Google Scholar 

  2. Z. Body, A. Kane, and A. Markus, Essentials of Investments, 4th ed., McGraw-Hill (2001).

  3. R. T. Rockafellar and S. Uryasev, “Optimization of conditional value-at-risk,” J. Risk, 2, 21–42 (2000).

    Google Scholar 

  4. V. I. Norkin, “On measuring and profiling catastrophic risks,” Cybern. Syst. Analysis, 42, No. 6, 839–850 (2006).

    Article  Google Scholar 

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

    Google Scholar 

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

    MATH  Google Scholar 

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

    Google Scholar 

  8. B. V. Norkin, “Calculating ruin probability of a non-Poisson risk process by the method of successive approximations,” Probl. Upravl. Inform., No. 2, 133–144 (2005).

  9. A. V. Boikov, “The Cramer-Lundberg model with stochastic premiums,” Teor. Veroyan. i yeyo Primen., 47, Issue 3, 549–553 (2002).

    Google Scholar 

  10. B. V. Norkin, “The method of successive approximations applied to find the nonbankruptcy probability for an insurance company with random premiums,” Cybern. Syst. Analysis, 42, No. 1, 98–110 (2006).

    Article  MATH  Google Scholar 

  11. V. I. Norkin, “Solving the Wiener-Hopf equation with a probabilistic kernel,” Cybern. Syst. Analysis, 42, No. 2, 195–201 (2006).

    Article  MATH  Google Scholar 

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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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Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 74–83, May–June 2007.

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Norkin, V.I. Self-insurance of investor under repeating catastrophic risks. Cybern Syst Anal 43, 377–383 (2007). https://doi.org/10.1007/s10559-007-0059-1

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  • DOI: https://doi.org/10.1007/s10559-007-0059-1

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