Communications for Statistical Applications and Methods

  • 제17권4호
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  • Pages.483-491
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  • 2010
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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Computing the Ruin Probability of Lévy Insurance Risk Processes in non-Cramér Models

  • Park, Hyun-Suk (Department of Finance and Information Statistics, Hallym University)
  • 투고 : 20100100
  • 심사 : 20100300
  • 발행 : 2010.07.31
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초록

This study provides the explicit computation of the ruin probability of a Le￠vy process on finite time horizon in Theorem 1 with the help of a fluctuation identity. This paper also gives the numerical results of the ruin probability in Variance Gamma(VG) and Normal Inverse Gaussian(NIG) models as illustrations. Besides, the paths of VG and NIG processes are simulated using the same parameter values as in Madan et al. (1998).

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참고문헌

  1. Alili, L. and Kyprianou, A. E. (2005). Some remarks on first passage of Levy processes, the Americal put and pasting principles, The Annals of Applied Probability, 15, 2062-2079. https://doi.org/10.1214/105051605000000377
  2. Bertoin, J. (1996). Levy Processes, Cambridge University Press.
  3. Bingham, N. H., Goldie, C. M. and Teugels, J. L. (1987). Regular Variation, Cambridge University Press, Cambridge.
  4. Doney, R. A. and Kyprianou, A. (2006). Overshoots and undershoots of Levy processes, The Annals of Applied Probability, 16, 91-106. https://doi.org/10.1214/105051605000000647
  5. Embrechts, P., Goldie, C. M. and Veraverbeke, N. (1979). Subexponentiality and infinite divisibility, Probability Theory and Related Fields, 49, 335-347.
  6. Fishman, G. S. (1996). Monte Carlo Methods: Concepts, Algorithms, and Applications, Springer.
  7. Grandell, J. (1991). Aspects of Risk Theory, Springer-Verlag, New York.
  8. Kluppelberg, C. (1989). Subexponential distributions and characterizations of related classes, Probability Theory and Related Fields, 82, 259-269. https://doi.org/10.1007/BF00354763
  9. Kluppelberg, C., Kyprianou, A. and Maller, R. (2004). Ruin probability and overshoots for general Levy insurance risk processes, The Annals of Applied Probability, 14, 1766-1801.
  10. Madan, D., Carr, P. and Chang, E. (1998). The variance gamma process and option pricing model, European Finance Review, 2, 79-105. https://doi.org/10.1023/A:1009703431535
  11. Madan, D. and Milne, F. (1991). Option pricing with VG martingale components, Mathematical Finance, 1, 39-55. https://doi.org/10.1111/j.1467-9965.1991.tb00018.x
  12. Madan, D. and Seneta, E. (1990). The variance gamma process model for share market returns, Journal of Business, 63, 511–524.
  13. Maller, R., Solomon, D. and Szimayer, A. (2006). A multinomial approximation for American option prices in Levy process models, Mathematical Finance, 160, 613-633.
  14. Park, H. S. and Maller, R. (2008). Moment and MGF convergence of overshoots and undershoots for Levy insurance risk processes, Advances in Applied Probability, 40, 716-733. https://doi.org/10.1239/aap/1222868183
  15. Sato, K. (1999). Levy Processes and Infinitely Divisible Distributions, Cambridge University Press, Cambridge.

피인용 문헌

  1. Ruin Probability in a Compound Poisson Risk Model with a Two-Step Premium Rule vol.18, pp.4, 2011, https://doi.org/10.5351/CKSS.2011.18.4.433
  2. Ruin Probability on Insurance Risk Models vol.24, pp.4, 2011, https://doi.org/10.5351/KJAS.2011.24.4.575