Gerber-Shiu discounted penalty function in a Sparre Andersen model with multi-layer dividend strategy
This paper studies a Sparre Andersen model in which the inter-claim times are generalized Erlang(n) distributed. We assume that the premium rate is a step function depending on the current surplus level. A piecewise integro-differential equation for the Gerber-Shiu discounted penalty function is derived and solved. Finally, to illustrate the solution procedure, explicit expression for the Laplace transform of the time to ruin is given when the inter-claim times are generalized Erlang(2) distributed and the claim amounts are exponentially distributed.
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- Lin, X. Sheldon & Willmot, Gordon E., 1999. "Analysis of a defective renewal equation arising in ruin theory," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 63-84, September.
- Albrecher, Hansjorg & Claramunt, M.Merce & Marmol, Maite, 2005. "On the distribution of dividend payments in a Sparre Andersen model with generalized Erlang(n) interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 324-334, October.
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- Dickson, David C. M. & Hipp, Christian, 2001. "On the time to ruin for Erlang(2) risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 333-344, December.
- Li, Shuanming & Garrido, Jose, 2004. "On ruin for the Erlang(n) risk process," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 391-408, June.
- Li, Shuanming & Garrido, Jose, 2004. "On a class of renewal risk models with a constant dividend barrier," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 691-701, December.
- Asmussen, Soren & Taksar, Michael, 1997. "Controlled diffusion models for optimal dividend pay-out," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 1-15, June.
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