Exponential and scale mixtures and equilibrium distributions

Ole Hesselager, Shaun Wang and Gordon Willmot

Scandinavian Actuarial Journal, 1998, vol. 1998, issue 2, 125-142

Abstract: In this article we discuss mixed exponential distributions and, more generally, scale mixtures with specific consideration the purpose of insurance modeling. Results are derived for equilibrium distributions (defined via stop-loss transforms) of mixed distributions. Some recursive relations are identified for the stop-loss transforms and moments of mixed exponential distributions. Explicit expressions are obtained for equilibrium gamma distributions with arbitrary shape parameter.

Date: 1998
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DOI: 10.1080/03461238.1998.10413998

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