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The optimal reinsurance treaty

Published online by Cambridge University Press:  29 August 2014

Karl Borch
Karl Borch*
Affiliation:
Bergen
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1. Some years ago I discussed optimal reinsurance treaties, without trying to give a precise definition of this term [1]. I suggested that a reinsurance contract could be called “most efficient” if it, for a given net premium, maximized the reduction of the variance in the claim distribution of the ceding company. I proved under fairly restricted conditions that the Stop Loss contract was most efficient in this respect.

I do not consider this a particularly interesting result. I pointed out at the time that there are two parties to a reinsurance contract, and that an arrangement which is very attractive to one party, may be quite unacceptable to the other.

2. In spite of my own reservations, it seems that this result —which I did not think deserved to be called a theorem—has caused some interest. Kahn [4] has proved that the result is valid under far more general conditions, and recently Ohlin [5] has proved that the result holds for a much more general class of measures of dispersion.

In view of these generalizations it might be useful to state once more, why I think the original result has relatively little interest. In doing so, it is by no means my purpose to reduce the value of the mathematical generalizations of Kahn and Ohlin. Such work has a value in itself, whether the results are immediately useful or not. I merely want to point out that there are other lines of research, which appear more promising, if our purpose is to develop a realistic theory of insurance.

Type
Subject three
Information
ASTIN Bulletin: The Journal of the IAA , Volume 5 , Issue 2 , May 1969 , pp. 293 - 297
Copyright
Copyright © International Actuarial Association 1969

References

REFERENCES

[1]Borch, Karl: “An Attempt to determine the Optimum Amount of Stop Loss Reinsurance”, Transactions of the XVI International Congress of Actuaries, Vol. I, pp. 597–610.Google Scholar
[2]Borch, Karl: “Reciprocal Reinsurance Treaties”, The ASTIN Bulletin, Vol. I, pp. 170–191.Google Scholar
[3]Borch, Karl: “The Utility Concept applied to the Theory of Insurance“, The ASTIN Bulletin, Vol. I, pp. 245–255.Google Scholar
[4]Kahn, Paul M.: “Some Remarks on a recent Paper by Borch”, The ASTIN Bulletin, Vol. I, pp. 265–272.Google Scholar
[5]Ohlin, Jan: “A Generalization of a Result by Borch and Kahn on the Optimal Properties of Stop Loss Reinsurance”, The ASTIN Bulletin, Vol. V, pp. 250.Google Scholar