On the Dividend Problem in a Risk Model with Delayed Claims

  • Wei Zou
  • Jie-hua Xie
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7030)


In this paper, a discrete time risk model with dividend payments is considered, in which the occurrences of the claims may be delayed. A system of differential equations with certain boundary conditions for the expected present value of dividend payments prior to ruin is derived and solved. Moreover, the closed form expressions are given when the claim size distributions belong to the rational family. The qualitative properties of ruin probabilities for this risk model are also obtained. Numerical results are provided to illustrate the applicability of the main result.


Discrete time risk model Delayed claim Dividend 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    De Finetti, B.: Su un Impostazione Alternativa Dell Teoria Collettiva Del Rischio. Transactions of the XVth International Congress of Actuaries (1957)Google Scholar
  2. 2.
    Gerber, H.U., Shiu, E.S.W., Yang, H.L.: An Elementary Approach to Discrete Models of Dividend Strategies. Insurance: Mathematics and Economics 46, 109–116 (2010)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Frostig, E.: Asymptotic Analysis of a Risk Process with High Dividend Barrier. Insurance: Mathematics and Economics 47, 21–26 (2010)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Liu, Z.M., Li, M.M., Ameer, S.: Methods for Estimating Optimal Dickson and Waters Modification Dividend Barrier. Economic Modelling 26, 886–892 (2009)CrossRefGoogle Scholar
  5. 5.
    Dassios, A., Wu, S.: On Barrier Strategy Dividends with Parisian Implementation Delay for Classical Surplus Processes. Insurance: Mathematics and Economics 45, 195–202 (2009)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Yin, G., Song, Q.S., Yang, H.: Stochastic Optimization Algorithms for Barrier Dividend Strategies. Journal of Computational and Applied Mathematics 223, 240–262 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Waters, H.R., Papatriandafylou, A.: Ruin Probabilities Allowing for Delay in Claims Settlement. Insurance: Mathematics and Economics 4, 113–122 (1985)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Yuen, K.C., Guo, J.Y.: Ruin Probabilities for Time-Correlated Claims in the Compound Binomial Model. Insurance: Mathematics and Economics 29, 47–57 (2001)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Xiao, Y.T., Guo, J.Y.: The Compound Binomial Risk Model with Time-Correlated Claims. Insurance: Mathematics and Economics 41, 124–133 (2007)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Xie, J.H., Zou, W.: Ruin Probabilities of a Risk Model with Time-Correlated Claims. Journal of the Graduate School of the Chinese Academy of Sciences 25, 319–326 (2008)Google Scholar
  11. 11.
    Zou, W., Xie, J.H.: On the Ruin Problem in an Erlang(2) Risk Model with Delayed Claims. In: Zhu, R., Zhang, Y., Liu, B.X., Liu, C.F. (eds.) ICICA 2010, Part II. CCIS, vol. 105, pp. 54–61. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Yuen, K.C., Guo, J.Y., Kai, W.N.: On Ultimate Ruin in a Delayed-Claims Risk Model. Journal of Applied Probability 42, 163–174 (2005)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Wei Zou
    • 1
  • Jie-hua Xie
    • 1
  1. 1.Department of ScienceNanChang Institute of TechnologyNanChangP.R. China

Personalised recommendations