Skip to main content
SpringerLink
Log in

On the Gerber-Shiu discounted penalty function for subexponential claims

  • Published:
Lithuanian Mathematical Journal Aims and scope Submit manuscript

Abstract

We obtain the asymptotics of the Gerber-Shiu discounted penalty function in the classical Lundberg model. We cosider claims from a class of subexponential distributions and find the asymptotics as the initial surplus x tends to infinity. The main term of the discounted penalty function ψ(x, δ) has different expressions in the cases where the interest rate δ > 0 and where δ = 0.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Drekic and G. E. Willmot, On the density and moments of the time of ruin with exponential claims, ASTIN Bulletin, 33(1), 11–21 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  2. P. Embrechts, C. Klüppelberg, and T. Mikosch, Modelling Extremal Events, Springer, Berlin (1997).

    MATH  Google Scholar 

  3. P. Embrechts and N. Veraverbeke, Estimates for the probability of ruin with special emphasis on the possibility of large claims, Insurance: Mathematics and Economics, 1(1), 55–72 (1982).

    Article  MATH  MathSciNet  Google Scholar 

  4. J. M. A. Garsia, Explicit solutions for survival probabilities in the classical risk model, ASTIN Bulletin, 35(1), 113–130 (2005).

    Article  MathSciNet  Google Scholar 

  5. H. Gerber and E. Shiu, On the time value of ruin, North Amer. Actuarial J., 2(1), 48–78 (1998).

    MATH  MathSciNet  Google Scholar 

  6. T. Mikosch, Non-Life Insurance Mathematics, Springer, Berlin (2004).

    MATH  Google Scholar 

  7. G. E. Willmot and D. C. M. Dickson, The Gerber-Shiu discounted penalty function in the stationary renewal risk model, Insurance: Mathematics and Economics, 32, 403–411 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  8. G. E. Willmot and X. S. Lin, Approximations for Compound Distributions with Insurance Applications, Springer, New York (2001).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Vilnius University, Naugarduko 24, LT-03225, Vilnius, Lithuania

    J. Šiaulys

  2. Joint-stock Company SAMPO Live Insurance, Geležinio Vilko 18A, LT-08104, Vilnius, Lithuania

    R. Asanavičiūutė

Authors
  1. J. Šiaulys
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Asanavičiūutė
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 4, pp. 598–605, October–December, 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Šiaulys, J., Asanavičiūutė, R. On the Gerber-Shiu discounted penalty function for subexponential claims. Lith Math J 46, 487–493 (2006). https://doi.org/10.1007/s10986-006-0044-9

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10986-006-0044-9

Keywords

Search

Navigation