De Finetti's retention problem for proportional reinsurance revisited

Glineur, François;Walhin, Jean-François
(2006) Blätter der DGVFM — Vol. 27, n° 3, p. 451-462 (2006)

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Abstract
We use convex optimization to provide a rigorous proof of de Finetti’s retention result for proportional reinsurance. We then extend this result to variable quota share reinsurance and surplus reinsurance with table of lines. We demonstrate by a numerical example that in general neither variable quota share reinsurance nor surplus reinsurance with table of lines may be considered as optimal reinsurance structures.
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Glineur, F., & Walhin, J.-F. (2006). De Finetti’s retention problem for proportional reinsurance revisited. Blätter der DGVFM, 27(3), 451-462. https://doi.org/10.1007/BF02809170 (Original work published 2006)