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Cybernetics and Systems Analysis

, Volume 50, Issue 2, pp 260–270 | Cite as

Systems Simulation Analysis and Optimization of Insurance Business

  • B. V. Norkin
Article

Abstract

Problems of computational actuarial mathematics, dynamic financial analysis, and optimization of insurance business and the possibility of their solution by means of parallel computing on graphics accelerators are discussed. The ruin probability and other performance criteria of an insurance company are estimated by the Monte Carlo method. In many cases, it is the only applicable method. Since the ruin probability is small enough, to achieve an acceptable estimate accuracy, an astronomical number of simulations may be required. Parallelization of the Monte Carlo method and the use of graphical accelerators allow us getting the desired result in a reasonable time. The results of numerical experiments on the developed system of actuarial modeling are presented, allowing the use of graphical accelerator that supports Nvidia CUDA 1.3 and higher.

Keywords

computational actuarial mathematics dynamic financial analysis simulation modeling optimization of insurance business risk process ruin probability efficient frontier parallel computing Monte Carlo method GPGPU CUDA 

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References

  1. 1.
    B. de Finetti, “Su un’impostazione alternativa della teoria collettiva del rischio,” in: Trans. 15th Intern. Congress of Actuaries, 2, New York (1957), pp. 433–443.Google Scholar
  2. 2.
    H. Schmidli, Stochastic Control in Insurance, Springer-Verlag, London (2008).MATHGoogle Scholar
  3. 3.
    N. L. Bowers, H. U. Gerber, J. C. Hickman, D. A. Jones, and C. J. Nesbitt, Actuarial Mathematics, Society of Actuaries, Itasca (1997).Google Scholar
  4. 4.
    V. Yu. Korolev, V. E. Bening, and S. Ya. Shorgin, Mathematical Fundamentals of Risk Theory [in Russian], Fizmatlit, Moscow (2011).Google Scholar
  5. 5.
    M. M. Leonenko, Yu. S. Mishura, Ya. M. Parkhomenko, and M. J. Yadrenko, Probability-Theoretical and Statistical Methods in Econometrics and Financial Mathematics [in Ukrainian], Informtekhnika, Kyiv (1995).Google Scholar
  6. 6.
    C. D. Daykin, T. Pentikainen, and M. Pesonen, Practical Risk Theory for Actuaries, Chapman and Hall, London – New York (1994).MATHGoogle Scholar
  7. 7.
    J. L. Teugels and B. Sundt (eds.), Encyclopedia of Actuarial Science, Wiley, Chichester (2004).MATHGoogle Scholar
  8. 8.
    R. Kaufmann, A. Gadmer, and R. Klett, “Introduction to dynamic financial analysis,” ASTIN Bull., 31, No. 1, 213–249 (2001).CrossRefGoogle Scholar
  9. 9.
    P. Blum and M. Dacorogna, “DFA — dynamic financial analysis,” in: J. L. Teugels and B. Sundt (eds.), Encyclopedia of Actuarial Science, Vol. 1, Wiley, Chichester (2004), pp. 3342–3355.Google Scholar
  10. 10.
    M. R. Hardy, “Dynamic financial modeling of an insurance enterprise,” in: J. L. Teugels and B. Sundt (eds.), Encyclopedia of Actuarial Science, Vol. 1, Wiley, Chichester (2004), pp. 3618–3628.Google Scholar
  11. 11.
    B. Norkin, “Parallel computations in insurance business optimization,” in: Proc. 1st Intern. Conf. on High Perform. Comput. (Oct. 12–14, 2011, Kyiv), Kyiv (2011), pp. 33–39.Google Scholar
  12. 12.
    B. V. Norkin, “Paralleling of the methods of insurance company bankruptcy risk assessment,” in: Teoriya Optym. Rishen’ [in Ukrainian], V. M. Glushkov Inst. of Cybernetics NANU, Kyiv (2010), pp. 33–39.Google Scholar
  13. 13.
    B. V. Norkin, “Ruin probability of a controlled autoregression process,” in: Komp. Matematyka [in Ukrainian], V. M. Glushkov Inst. of Cybernetics NANU, Kyiv (2011), pp. 142–150.Google Scholar
  14. 14.
    B. V. Norkin, “Actuarial computing with the use of graphic processors,” in: Trans. Intern. Conf. on High Performance Computing (HPC-UA 2012, Kyiv, October, 10, 2012), NANU, Kyiv (2012), pp. 268–274.Google Scholar
  15. 15.
    B. V. Norkin, “On performing actuarial calculations on GPU,” in: Visn. NTUU “KPI,” Inform., Upravl. ta Obchysl. Tekhn., Zb. Nauk. Prats’, No. 56 (2012), pp. 113–119.Google Scholar
  16. 16.
    A. V. Boreskov, A. A. Kharlamov, N. D. Markovskii et al., Parallel Computing on GPU. CUDA Architecture and Program Model [in Russian], Izd. Mosk. Univer., Moscow (2012).Google Scholar
  17. 17.
    B. V. Norkin, “Mathematical models for insurance optimization,” Cybern. Syst. Analysis, 47, No. 1, 117–133 (2011).CrossRefMathSciNetGoogle Scholar
  18. 18.
    B. V. Norkin, “Insurance portfolio optimization,” Prikl. Statistika. Aktuar. ta Fin. Matem., No. 1–2, 197–203 (2011).Google Scholar
  19. 19.
    G. B. Dantzig, “Need to do planning under uncertainty and the possibility of using parallel processors for this purpose,” Ekonom.-Mat. Obzor, 23, 121–135 (1987).MathSciNetGoogle Scholar
  20. 20.
    G. B. Dantzig and P. W. Glynn, “Parallel processors for planning under uncertainty,” Ann. Oper. Res., 22, 1–21 (1990).CrossRefMATHMathSciNetGoogle Scholar
  21. 21.
  22. 22.
    Li J., Hu X., Zhanlong Pang Z., and Qian K., “A parallel ant colony optimization algorithm based on fine-grained model with gpu-acceleration,” Intern. J. Innov. Comput., Inform. and Control, 5, No. 11(A), 3707–3716 (2009).Google Scholar
  23. 23.
    E. A. Nurminskii and P. L. Pozdnyak, “Solving the problem of searching for the least distance to a polytope with the use of graphical accelerators,” Vychisl. Tekhnol., 16, Issue 5, 80–88 (2011).Google Scholar
  24. 24.
    Law of Ukraine “On insurance,” Vidom. Verkh. Rady Ukrainy, No. 18, p. 78 (1996), http://zakon1.rada.gov.ua/laws/show/85/96-Bp.
  25. 25.
    A. I. Zaletov, Insurance in Ukraine [in Russian], Intern. Agency “BeeZone,” Kyiv (2002).Google Scholar
  26. 26.
  27. 27.
    A. Nakonechnyi, “Optimization of risk processes,” Cybern. Syst. Analysis, 32, No. 5, 641–646 (1996).CrossRefMATHMathSciNetGoogle Scholar
  28. 28.
    P. Cízek, W. Hardle, and R. Weron (eds.), Statistical Tools for Finance and Insurance, Springer, New York (2005).MATHGoogle Scholar
  29. 29.
    H. R. Waters, “Some mathematical aspects of reinsurance,” Insurance: Math. Econ., No. 2, 17–26 (1983).Google Scholar
  30. 30.
    IBM ILOG CPLEX V12.1. User’s manual for CPLEX, Intern. Business Machines Corp. (2009).Google Scholar
  31. 31.
    W. Hoeffding, “Probability inequalities for sums of bounded random variables,” J. Amer. Statist. Assoc., 58, 13–30 (1963).CrossRefMATHMathSciNetGoogle Scholar
  32. 32.
    NVIDIA, CUDA CURAND Library (2010).Google Scholar
  33. 33.
    Intel Digital Random Number Generator (DRNG): Software Implementation Guide, http://software.intel.com/en-us/articles/intel-digital-random-number-generator-drng-software-implementation-guide/.

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine

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