Abstract
In this paper, we consider the classical surplus process with a constant dividend barrier and a dependence structure between the claim amounts and the inter-claim times. We derive an integro-differential equation with boundary conditions. Its solution is expressed as the Gerber-Shiu discounted penalty function in the absence of a dividend barrier plus a linear combination of a finite number of linearly independent particular solutions to the associated homogeneous integro-differential equation. Finally, we obtain an explicit solution when the claim amounts are exponentially distributed and we investigate the effects of dependence on ruin quantities.
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Cossette, H., Marceau, E. & Marri, F. Constant Dividend Barrier in a Risk Model with a Generalized Farlie-Gumbel-Morgenstern Copula. Methodol Comput Appl Probab 13, 487–510 (2011). https://doi.org/10.1007/s11009-010-9168-9
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DOI: https://doi.org/10.1007/s11009-010-9168-9
Keywords
- Compound Poisson risk model
- Copula
- Generalized Farlie-Gumbel-Morgenstern copulas
- Constant dividend barrier
- Ruin theory
- Dependence models
- Gerber-Shiu discounted penalty function