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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- Albrecher, Hansjörg & Hartinger, Jürgen & Thonhauser, Stefan, 2007. "On Exact Solutions for Dividend Strategies of Threshold and Linear Barrier Type in a Sparre Andersen Model," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 37(02), pages 203-233, November.
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