Ordering of risks through loss ratios

Using a model of financial insurance a stable retention ratio is associated to the underwriting return ratio of an insurable risk. It is the most stable retention ratio needed to cover the risk of an over-loss by self-finance. A recursive algorithm to evaluate it is derived. Two new total ordering r...

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Bibliographic Details
Published in:Insurance, mathematics & economics mathematics & economics, 1992-04, Vol.11 (1), p.49-54
Main Author: Hurlimann, Werner
Format: Article
Language:English
Subjects:
Economic models
Economic theory
Insurable risks
Insurance companies
Insurance premiums
Loss ratio
Ordering of risks
Retention
Return order
Risk
Stability index
Studies
Underwriting
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Summary:Using a model of financial insurance a stable retention ratio is associated to the underwriting return ratio of an insurable risk. It is the most stable retention ratio needed to cover the risk of an over-loss by self-finance. A recursive algorithm to evaluate it is derived. Two new total ordering relations are defined. The first, return order shows the relation between the stable retention ratios for different risks. It preserves stop-loss order between loss ratios. The mean—variance approximation of the stable retention ratio defines a stability return index, which is shown to induce a total stable return order on risks which preserves stop-loss order between loss ratios with equal mean. The actuarial use of the new concepts is illustrated by some examples.
ISSN:0167-6687
1873-5959
DOI:10.1016/0167-6687(92)90087-R