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In this article, the authors 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.
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Yushkevich can also be applied to certain models where control of the flow is possible. The method consists in a transformation to a model without control of the flow by a kind of time change.
The problem of determining optimal retention levels for a non-life portfolio consisting of a number of independent sub-portfolios was first discussed by de Finetti (1946). He considered retention levels to be optimal if they minimized the variance of the insurer's profit from the portfolio subject t
Yushkevich can also be applied to certain models where control of the flow is possible. The method consists in a transformation to a model without control of the flow by a kind of time change.