Acta Mathematicae Applicatae Sinica

, Volume 21, Issue 1, pp 153–156 | Cite as

The Finite Time Ruin Probability with the Same Heavy-tailed Insurance and Financial Risks

Original Papers

Abstract

This note complements a recent study in ruin theory with risky investment by establishing the same asymptotic estimate for the finite time ruin probability under a weaker restriction on the financial risks. In particular, our result applies to a critical case that the insurance and financial risks have Pareto-type tails with the same regular index.

Keywords

asymptotics heavy tails finite time ruin probability 

2000 MR Subject Classification

62P05 62E10 91B30 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Cai, J., Tang, Q.H. On max-sum equivalence and convolution closure of heavy-tailed distributions and their applications. Journal of Applied Probability, 41:117–130 (2004)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Cline, D.B.H., Samorodnitsky, G. Subexponentiality of the product of independent random variables. Stochastic Processes and their Applications, 49:75–98 (1994)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Embrechts, P., Klüppelberg, C., Mikosch, T. Modelling Extremal Events for Insurance and Finance. Springer-Verlag, Berlin, 1997Google Scholar
  4. 4.
    Nyrhinen, H. On the ruin probabilities in a general economic environment. Stochastic Processes and their Applications, 83:319–330 (1999)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Nyrhinen, H. Finite and infinite time ruin probabilities in a stochastic economic environment. Stochastic Processes and their Applications, 92:265–285 (2001)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Tang, Q. H., Tsitsiashvili, G. Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks. Stochastic Processes and their Applications, 108:299–325 (2003)MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.School of Economics and ManagementGuangdong University of TechnologyGuangzhou 510090China

Personalised recommendations