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New Applied Probability Models and Their Stability

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Analytical and Computational Methods in Probability Theory (ACMPT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10684))

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Abstract

New models were developed in actuarial sciences during the last two decades. They include different notions of insurance company ruin (bankruptcy) and other objective functions evaluating the company performance. Several types of decision (such as dividends payment, reinsurance, investment) are used for optimization of company functioning. Therefore it is necessary to be sure that the model under consideration is stable with respect to parameters fluctuation and perturbation of underlying stochastic processes. The aim of the paper is description of methods for investigation of these problems and presentation of recent results concerning some insurance models.

The work is partially supported by RFBR grant No. 17-01-00468.

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References

  1. Rachev, S.T., Stoyanov, S.V., Fabozzi, F.J.: Advanced Stochastic Models, Risk Assessment, Portfolio Optimization. Wiley, Hoboken (2008)

    Google Scholar 

  2. Bulinskaya, E.: New research directions in modern actuarial sciences. In: Panov, V. (ed.) Modern Problems of Stochastic Analysis and Statistics - Festschrift in Honor of Valentin Konakov. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-65313-6_15

    Google Scholar 

  3. D’Arcy, S.P.: On becoming an actuary of the fourth kind. Proc. Casualty Actuar. Soc. 177, 745–754 (2005)

    Google Scholar 

  4. Cruz, M.G., Peters, G.W., Shevchenko, P.V.: Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk. Wiley, Hoboken (2015)

    Book  Google Scholar 

  5. Avanzi, B., Gerber, H.U., Shiu, E.S.W.: Optimal dividends in the dual model. Insur.: Math. Econ. 41(1), 111–123 (2007)

    MathSciNet  MATH  Google Scholar 

  6. Bayraktar, E., Egami, M.: Optimizing venture capital investment in a jump diffusion model. Math. Methods Oper. Res. 67(1), 21–42 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Asmussen, S., Albrecher, H.: Ruin Probabilities, 2nd edn. World Scientific, Hackensack (2010)

    Book  MATH  Google Scholar 

  8. De Finetti, B.: Su un’impostazione alternativa della teoria collettiva del rischio. In: Transactions of the XV-th International Congress of Actuaries, vol. 2, pp. 433–443 (1957)

    Google Scholar 

  9. Avanzi, B.: Strategies for dividend distribution: a review. North Am. Actuar. J. 13(2), 217–251 (2009)

    Article  MathSciNet  Google Scholar 

  10. Bulinskaya, E.V.: On a cost approach in insurance. Rev. Appl. Ind. Math. 10(2), 376–386 (2003). (in Russian)

    MATH  Google Scholar 

  11. Breuer, L., Badescu, A.: A generalised Gerber-Shiu measure for Markov-additive risk processes with phase-type claims and capital injections. Scand. Actuar. J. 2014(2), 93–115 (2014)

    Article  MathSciNet  Google Scholar 

  12. Abdallah, A., Boucher, J.P., Cossette, H.: Modeling dependence between loss triangles with hierarchical Archimedean copulas. ASTIN Bull. 45, 577–599 (2015)

    Article  MathSciNet  Google Scholar 

  13. Quang, P.D.: Ruin probability in a generalized risk process under interest force with homogenous Markov chain premiums. Int. J. Stat. Probab. 2(4), 85–92 (2013)

    Article  Google Scholar 

  14. Sandström, A.: Handbook of Solvency for Actuaries and Risk Managers: Theory and Practice. Chapman and Hall/CRC Press, Boca Raton (2011)

    MATH  Google Scholar 

  15. Czarna, I., Palmowski, Z.: Ruin probability with Parisian delay for a spectrally negative Lévy risk process. J. Appl. Probab. 48, 984–1002 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. Lkabous, M.A., Czarna, I., Renaud, J.-F.: Parisian Ruin for a Refracted Lévy Process. arXiv:1603.09324v1 [math.PR], 30 March 2016

  17. Landriault, D., Renaud, J.-F., Zhou, X.: Insurance risk models with Parisian implementation delays. Methodol. Comput. Appl. Probab. 16(3), 583–607 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  18. Guérin, H., Renaud, J.-F.: On Distribution of Cumulative Parisian Ruin. arXiv:1509.06857v1 [math.PR], 23 September 2015

  19. Gerber, H.U.: Der Einfluss von Zins auf die Ruinwahrscheinlichkeit. Mitteilungen der Vereinigung schweizerischer Versicherungsmathematiker 71(1), 63–70 (1971)

    MATH  Google Scholar 

  20. Fu, D., Guo, Y.: On the compound Poisson model with debit interest under absolute ruin. Int. J. Sci. Res. (IJSR) 5(6), 1872–1875 (2016)

    Article  Google Scholar 

  21. Albrecher, H., Gerber, H.U., Shiu, E.S.W.: The optimal dividend barrier in the Gamma-Omega model. Eur. Actuar. J. 1, 43–55 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  22. Saltelli, A., Ratto, M., Campolongo, T., Cariboni, J., Gatelli, D., Saisana, M., Tarantola, S.: Global Sensitivity Analysis. The Primer. Wiley, Hoboken (2008)

    MATH  Google Scholar 

  23. Dassios, A., Wu, Sh.: Parisian ruin with exponential claims, 1 July 2008. stats.lse.ac.uk/angelos/docs/exponentialjump.pdf

  24. Gerber, H.U.: When does the surplus reach a given target? Insur.: Math. Econ. 9, 115–119 (1990)

    MathSciNet  MATH  Google Scholar 

  25. Bateman, H.: Table of Integral Transforms, vol. I. McGraw-Hill Book Company, INC, New York (1954)

    Google Scholar 

  26. Gerber, H.U., Shiu, E.S.W.: The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin. Insur.: Math. Econ. 21, 129–137 (1997)

    MathSciNet  MATH  Google Scholar 

  27. Liu, D., Liu, Z.: Dividend problems with a barrier strategy in the dual risk model until bankruptcy. J. Appl. Math. 2014, Article ID 184098 (2014)

    Google Scholar 

  28. Rachev, S.T., Klebanov, L., Stoyanov, S.V., Fabozzi, F.: The Methods of Distances in the Theory of Probability and Statistics. Springer, New York (2013). https://doi.org/10.1007/978-1-4614-4869-3

    Book  MATH  Google Scholar 

  29. Bulinskaya, E., Gusak, J.: Optimal control and sensitivity analysis for two risk models. Commun. Stat. Simul. Comput. 45(5), 1451–1466 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  30. Bulinskaya, E.V.: Stochastic insurance models: their optimality and stability. In: Skiadas, C.H. (ed.) Advances in Data Analysis, pp. 129–140. Birkhäuser, Boston (2010)

    Chapter  Google Scholar 

  31. Bulinskaya, E.V.: Sensitivity analysis of some applied models. Pliska Stud. Math. Bulg. 18, 57–90 (2007)

    MathSciNet  Google Scholar 

  32. Bulinskaya, E.V.: Systems stability and optimal control. J. Math. Sci. 92(3), 3857–3872 (1998)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Probability Theory, Faculty of Mathematics and Mechanics, Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119234, Russia

    Ekaterina Bulinskaya

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  1. Ekaterina Bulinskaya
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Correspondence to Ekaterina Bulinskaya .

Editor information

Editors and Affiliations

  1. Department of Applied Probability and Informatics, RUDN University, Moscow, Russia

    Vladimir V. Rykov

  2. City University of Hong Kong, Hong Kong, Hong Kong

    Nozer D. Singpurwalla

  3. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

    Andrey M. Zubkov

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Bulinskaya, E. (2017). New Applied Probability Models and Their Stability. In: Rykov, V., Singpurwalla, N., Zubkov, A. (eds) Analytical and Computational Methods in Probability Theory. ACMPT 2017. Lecture Notes in Computer Science(), vol 10684. Springer, Cham. https://doi.org/10.1007/978-3-319-71504-9_20

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  • DOI: https://doi.org/10.1007/978-3-319-71504-9_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71503-2

  • Online ISBN: 978-3-319-71504-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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