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Non-optimality of a linear combination of proportional and non-proportional reinsurance

For the subclass of reinsurance contracts with maximum deductible contained in the class of all bivariate comonotonic risk-exchange structures associated to a given risk, we consider optimality with respect to a long-term actuarial mean self-financing property and competitiveness of the insurance pr...

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Published in:	Insurance, mathematics & economics mathematics & economics, 1999-05, Vol.24 (3), p.219-227
Main Author:	Hurlimann, W
Format:	Article
Language:	English
Subjects:	Actuaries Comonotonicity Contracts Deductible coverage Hedging Inequality Inequality of Bowers Inequality of Kremer Inequality of Schmitter Insurance Linear models Mean self-financing property Optimal deductible Optimization Perfect hedge Reinsurance Risk Studies Total splitting risk
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container_title	Insurance, mathematics & economics
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creator	Hurlimann, W
description	For the subclass of reinsurance contracts with maximum deductible contained in the class of all bivariate comonotonic risk-exchange structures associated to a given risk, we consider optimality with respect to a long-term actuarial mean self-financing property and competitiveness of the insurance premium. For arbitrary varying risks, the linear combination of proportional and stop-loss reinsurance is not optimal unless it is a pure stop-loss contract, at least if the variance premium principle is used to set insurance prices. By known distribution of the risk, it is shown how an optimal deductible of a stop-loss contract can be determined. Some applications to insurance and finance are briefly mentioned.
doi_str_mv	10.1016/S0167-6687(98)00054-7
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source	International Bibliography of the Social Sciences (IBSS); Backfile Package - Economics, Econometrics and Finance (Legacy) [YET]; Elsevier SD Backfile Mathematics; Elsevier
subjects	Actuaries Comonotonicity Contracts Deductible coverage Hedging Inequality Inequality of Bowers Inequality of Kremer Inequality of Schmitter Insurance Linear models Mean self-financing property Optimal deductible Optimization Perfect hedge Reinsurance Risk Studies Total splitting risk
title	Non-optimality of a linear combination of proportional and non-proportional reinsurance
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