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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Bibliographic Details
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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Summary: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.
ISSN:0167-6687
1873-5959
DOI:10.1016/S0167-6687(98)00054-7