Insurance Portfolio Containing a Catastrophe Bond and an External Help with Imprecise Level—A Numerical Analysis

  • Maciej RomaniukEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 643)


In this paper, an integrated insurer’s portfolio, which consists of a few layers of insurance and financial instruments, is numerically analysed. A future behaviour of such a portfolio is related to stochastic processes (like a random interest rate yield and uncertain catastrophic losses), therefore the Monte Carlo (MC) approach is applied. A special attention is paid to a problem of a share of catastrophe bonds in such a portfolio and to an analysis of an influence of an additional layer—an external (e.g. governmental) help. Some important measures of an insurer’s risk (like a probability of his bankruptcy) are then numerically analysed. In considered examples, apart from strictly crisp sets of parameters, also fuzzy numbers are used to model an imprecise information concerning the possible external help.


Risk process Insurance portfolio Catastrophe bond Monte Carlo simulations Probability of ruin Governmental help Fuzzy numbers 


  1. 1.
    Chan, K.C., Karolyi, G.A., Longstaff, F.A., Sanders, A.B.: An empirical comparison of alternative models of the short-term interest rate. J. Finan. 47(3), 1209–1227 (1992)CrossRefGoogle Scholar
  2. 2.
    Chernobai, A., Burnecki, K., Rachev, S., Trück, S., Weron, R.: Modeling catastrophe claims with left-truncated severity distributions. Comput. Stat. 21(3), 537–555 (2006). doi: 10.1007/s00180-006-0011-2 CrossRefzbMATHGoogle Scholar
  3. 3.
    Ermoliev, Y.M., Ermolieva, T.Y., MacDonald, G.J., Norkin, V.I.: Stochastic optimization of insurance portfolios for managing exposure to catastrophic risks. Ann. Oper. Res. 99(1), 207–225 (2000). doi: 10.1023/A:1019244405392 MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Gil, M.A., Hryniewicz, O.: Statistics with imprecise data. In: Meyers, R.A. (ed.) Encyclopedia of Complexity and Systems Science, pp. 8679–8690. Springer, Heidelberg (2009)Google Scholar
  5. 5.
    Homem-de-Mello, T., Bayraksan, G.: Monte Carlo sampling-based methods for stochastic optimization. Surv. Oper. Res. Manag. Sci. 19(1), 56–85 (2014). doi: 10.1016/j.sorms.2014.05.001 MathSciNetGoogle Scholar
  6. 6.
    Hryniewicz, O., Kaczmarek, K., Nowak, P.: Bayes statistical decisions with random fuzzy data–an application for the Weibull distribution. Eksploatacja i Niezawodnosc (Maintenance and Reliability) 17(4), 610–616 (2015). doi: 10.17531/ein.2015.4.18 CrossRefGoogle Scholar
  7. 7.
    Nowak, P., Pawłowski, M.: Option pricing with application of Levy processes and the minimal variance equivalent martingale measure under uncertainty. IEEE Trans. Fuzzy Syst. 25(2), 402–416 (2017). doi: 10.1109/TFUZZ.2016.2637372 CrossRefGoogle Scholar
  8. 8.
    Nowak, P., Romaniuk, M.: Pricing and simulations of catastrophe bonds. Insur. Math. Econ. 52(1), 18–28 (2013). doi: 10.1016/j.insmatheco.2012.10.006 MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Nowak, P., Romaniuk, M.: Application of Levy processes and Esscher transformed martingale measures for option pricing in fuzzy framework. J. Comput. Appl. Math. 263, 129–151 (2014). doi: 10.1016/ MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Nowak P., Romaniuk, M.: Valuing catastrophe bond involving correlation and CIR interest rate model. Computational and Applied Mathematics (2016). doi: 10.1007/s40314-016-0348-2
  11. 11.
    Nowak, P., Romaniuk, M.: Catastrophe bond pricing for the two-factor Vasicek interest rate model with automatized fuzzy decision making. Soft Comput. 21(10), 2575–2597 (2017). doi: 10.1007/s00500-015-1957-1 CrossRefGoogle Scholar
  12. 12.
    Romaniuk, M.: On simulation of maintenance costs for water distribution system with fuzzy parameters. Eksploatacja i Niezawodnosc (Maintenance and Reliability) 18(4), 514–527 (2016). doi: 10.17531/ein.2016.4.6 CrossRefGoogle Scholar
  13. 13.
    Romaniuk, M.: Analysis of the insurance portfolio with an embedded catastrophe bond in a case of uncertain parameter of the insurer’s share. In: Wilimowska, Z., Borzemski, L., Grzech, A., Świątek, J. (eds.) Information Systems Architecture and Technology: Proceedings of 37th International Conference on Information Systems Architecture and Technology—ISAT 2016—Part IV. Advances in Intelligent Systems and Computing, vol. 524, pp. 33–43. Springer International Publishing (2017). doi: 10.1007/978-3-319-46592-0_3
  14. 14.
    Romaniuk, M., Nowak, P.: Monte Carlo Methods: Theory, Algorithms and Applications to Selected Financial Problems. ICS PAS, Warszawa (2015)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Systems Research InstitutePolish Academy of SciencesWarszawaPoland

Personalised recommendations