98
Views
9
CrossRef citations to date
0
Altmetric
Original Articles

On the expected discounted penalty function for a risk model with dependence under a multi-layer dividend strategy

&
Pages 1898-1915 | Received 03 Nov 2014, Accepted 10 Mar 2015, Published online: 16 Mar 2016

References

  • Albrecher, H., Boxma, O.J. (2004). A ruin model with dependence between claim sizes and claim intervals. Insurance: Math. Econ. 35:245–254.
  • Albrecher, H., Hartinger, J. (2007). A risk model with multi-layer dividend strategy. North Am. Actuarial J. 11:43–64.
  • Albrecher, H., Hartinger, J., Tichy, R. (2005). On the distribution of dividend payments and the discounted penalty function in a risk model with linear dividend barrier. Scand. Actuarial J. 2:103–126.
  • Boudreault, M., Cossette, H., Landrault, D., Marceau, E. (2006). On a risk model with dependence between interclaim arrivals and claim sizes. Scand. Actuarial J. 5:265–285.
  • Cossette, H., Marceau, E., Marri, F. (2010). Analysis of ruin measures for the classical compound Poisson risk model with dependence. Scand. Actuarial J. 3:221–245.
  • Cossette, H., Marceau, E., Marri, F. (2014). On a compound Poisson risk model with dependence and in the presence of a constant dividend barrier. Appl. Stochastic Models Bus. Ind. 30:82–98.
  • De Finetti, B. (1957). Su un’ impostazione alternative della teoria collective del rischio. Proc. Trans. XV Int. Congress Actuaries 2:433–443.
  • Dickson, D.C.M., Waters, H.R. (2004). Some optimal dividend problems. ASTIN Bull. 34:49–74.
  • Dickson, D.C.M., Hipp, C. (2001). On the time to ruin for Erlang(2) risk processes. Insurance: Math. Econ. 29:333–344.
  • Gerber, H.U., Shiu, E.S.W. (1998). On the time value of ruin. North Am. Actuarial J. 2:48–78.
  • Gerber, H.U., Shiu, E.S.W. (2006). On optimal dividend strategies in the compound Poisson model. North Am. Actuarial J. 10:76–93.
  • Gebizlioglu, O., Yagci, B. (2008). Tolerance intervals for quantities of bivariate risks and risk measurement. Insurance: Math. Econ. 42:1022–1027.
  • Geluk, J., Tang, Q. (2009). Asymptotic tail probabilities of sums of dependent subexponential random variables. J. Theor. Probab. 22:871–882.
  • Landriault, D. (2008). Constant dividend barrier in a risk model with interclaim-dependent claim sizes. Insurance: Math. Econ. 42:31–38.
  • Li, S., Garrido, J. (2004). On ruin for Erlang(n) risk process. Insurance: Math. Econ. 34:391–408.
  • Lin, X.S., Pavlova, K.P. (2006). The compound Poisson risk model with a threshold dividend strategy. Insurance: Math. Econ. 38:57–80.
  • Lin, X.S., Sendova, K.P. (2008). The compound Poisson risk model with multiple thresholds. Insurance: Math. Econ. 42:617–627.
  • Lin, X.S., Willmot, G.E. (1999). Analysis of a defective renewal equation arising in ruin theory. Insurance: Math. Econ. 25:63–84.
  • Lu, Y., Li, S. (2009). The Markovian regime-switching model with a threshold dividend strategy. Insurance: Math. Econ. 44:296–303.
  • Nelsen, R.B. (2006). An Introduction to Copulas (2nd ed.), Springer Series in Statistics. New York: Springer-Verlag.
  • Shi, Y.F., Liu, P., Zhang, C.S. (2013). On the compound Poisson risk model with dependence and a threshold dividend strategy. Stat. Probab. Lett. 83:1998–2006.
  • Tang, Q., Vernic, R. (2007). The impact on ruin probabilities of the association structure among financial risks. Stat. Probab. Lett. 77:1522–1525.
  • Willmot, G.E., Lin, X.S. (2001). Lundberg Approximations for Compound Distributions with Insurance Applications. Lecture Notes in Statistics. New York: Springer-Verlag.
  • Xie, J.H., Zou, W. (2010). Expected present value of total dividends in a delayed claims risk model under stochastic interest rates. Insurance: Math. Econ. 46:415–422.
  • Xie, J.H., Zou, W. (2011). On the expected discounted penalty function for the compound Poisson risk model with delayed claims. J. Comput. Appl. Math. 235:2392–2404.
  • Xie, J.H., Zou, W. (2013). On a risk model with random incomes and dependence between claim sizes and claim intervals. Indagationes Math. 24:557–580.
  • Yang, H., Zhang, Z.M. (2009). On a perturbed Sparre Andersen risk model with multi-layer dividend strategy. J. Comput. Appl. Math. 232:612–624.
  • Yang, H., Zhang, Z.M. (2008). Gerber–Shiu discounted penalty function in a Sparre Andersen model with multi-layer dividend strategy. Insurance: Math. Econ. 42:582–593.
  • Zhang, Z.M., Yang, H. (2011). Gerber–Shiu analysis in a perturbed risk model with dependence between claim sizes and interclaim times. J. Comput. Appl. Math. 235:1189–1204.
  • Zhou, M., Cai, J. (2009). A perturbed risk model with dependence between premium rates and claim sizes. Insurance: Math. Econ. 45:382–392.
  • Zhou, X. (2007). Classical risk model with multi-layer premium rate. Actuarial Res. Clear. House 1. http://www.soa.org/files/pdf/ARCH07v41n1III.pdf
  • Zou, W., Gao, J.W., Xie, J.H. (2014). On the expected discounted penalty function and optimal dividend strategy for a risk model with random incomes and interclaim-dependent claim sizes. J. Comput. Appl. Math. 255:270–281.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.