Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

A NOTE ON THE SEVERITY OF RUIN IN THE RENEWAL MODEL WITH CLAIMS OF DOMINATED VARIATION

  • Tang, Qihe (Department of Quantitative Economics, University of Amsterdam)
  • Published : 2003.11.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper investigates the tail asymptotic behavior of the severity of ruin (the deficit at ruin) in the renewal model. Under the assumption that the tail probability of the claimsize is dominatedly varying, a uniform asymptotic formula for the tail probability of the deficit at ruin is obtained.

Keywords

References

  1. Ruin probabilities S.Asmussen
  2. Statist. Probab. Lett. v.59 no.4 Approximations for moments of deficit at ruin with exponential and subexponential claims Y.B.Cheng;Q.H.Tang;H.L.Yang https://doi.org/10.1016/S0167-7152(02)00234-1
  3. Modelling Extremal Events for Insurance and Finance P.Embrechts;C.kluppelberg;T.Mikosch
  4. Insurance Math. Econom. v.1 no.1 Estimates for the probability of ruin with special emphasis on the possibility of large claims P.Embrechts;N.Veraverbeke https://doi.org/10.1016/0167-6687(82)90021-X
  5. J. Appl. Probab. v.21 no.1 A property of longtailed distributions P.Embrechts;E.Omey https://doi.org/10.2307/3213666
  6. Astin Bull. v.17 no.2 On the probability and severity of ruin H.U.Gerber;M.J.Goovaerts;R.Kaas https://doi.org/10.2143/AST.17.2.2014970
  7. Scand. Actuar. J. no.1 Two-sided bounds of ruin probabilities V.V.Kalashnikov
  8. Insurance Math. Econom. v.14 no.1 On some measures of the severity of ruin in the classical Poisson model P.Picard https://doi.org/10.1016/0167-6687(94)00006-9
  9. Stochastic Processes for Insurance and Finance T.Rolski;H.Schmidli;V.Schmidt;J.Teugels
  10. Austin Bull. v.29 no.2 On the distribution of the surplus prior to and to ruin H.Schmidli https://doi.org/10.2143/AST.29.2.504613
  11. Doctoral Thesis, University of Science and Technology of China Extremal values of risk processes for insurance and finance:with special emphasis on the possibility of large claims Q.H.Tang
  12. Stochastic Processes Appl. v.5 no.1 Asymptotic behaviour of Wiener-Hopf factors of a random walk N.Veraverbeke https://doi.org/10.1016/0304-4149(77)90047-3
  13. Insurance Math. Econom. v.23 no.1 Exact and approximate properties of the distribution of surplus before and after ruin G.E.Willmot;X.S.Lin https://doi.org/10.1016/S0167-6687(98)00030-4

Cited by

  1. The deficit at ruin in the Sparre Andersen model with interest vol.23, pp.1-2, 2007, https://doi.org/10.1007/BF02831960
  2. The Uniform Asymptotics of the Overshoot of a Random Walk with Light-Tailed Increments vol.42, pp.5, 2013, https://doi.org/10.1080/03610926.2011.585010
  3. The overshoot of a random walk with negative drift vol.77, pp.2, 2007, https://doi.org/10.1016/j.spl.2006.06.005
  4. The Uniform Local Asymptotics of the Overshoot of a Random Walk with Heavy-Tailed Increments vol.25, pp.3, 2009, https://doi.org/10.1080/15326340903088859
  5. Estimates for the overshoot of a random walk with negative drift and non-convolution equivalent increments vol.83, pp.6, 2013, https://doi.org/10.1016/j.spl.2013.02.015
  6. Random walks with non-convolution equivalent increments and their applications vol.374, pp.1, 2011, https://doi.org/10.1016/j.jmaa.2010.08.040