Constant Dividend Barrier in a Risk Model with a Generalized Farlie-Gumbel-Morgenstern Copula

Hélène Cossette, Etienne Marceau () and Fouad Marri
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Hélène Cossette: Université Laval
Etienne Marceau: Université Laval
Fouad Marri: Université Laval

Methodology and Computing in Applied Probability, 2011, vol. 13, issue 3, 487-510

Abstract: 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.

Keywords: Compound Poisson risk model; Copula; Generalized Farlie-Gumbel-Morgenstern copulas; Constant dividend barrier; Ruin theory; Dependence models; Gerber-Shiu discounted penalty function; Primary 62P05; Secondary 60K05 (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s11009-010-9168-9

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