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Exchange de Risques entre Assureurs et Theorie des Jeux

Published online by Cambridge University Press:  29 August 2014

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Summary

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A theorem of Borch characterizing Pareto-optimal treaties in a reinsurance market is extended to the case of non-differentiable utilities. Sufficient conditions for the existence of a solution to the equations are established. The problem is then shown to be identical to the determination of the value of a cooperative non-transferable m-person game. We show how to compute the Shapley value of this game, then we introduce a new value concept. An example illustrates both methods.

Type
Research Article
Copyright
Copyright © International Actuarial Association 1977

References

Bibliographie

[1]Borch, K., “The safety loading of reinsurance premiumsSkandinavsk Aktuarietidskrift, 43 (1960), pp. 163184.Google Scholar
[2]Borch, K., “Reciprocal reinsurance treatiesASTIN Bulletin, 1 (1960) pp. 170191.CrossRefGoogle Scholar
[3]Borch, K., “Equilibrium in a reinsurance marketEconometrıca, 30 (1962), pp. 424444.CrossRefGoogle Scholar
[4]Borch, K., “Reciprocal Reinsurance Treaties seen as a Two-Person Cooperative GameSkandinavsk Aktuarietidskrift, 43 (1960), pp. 2958.Google Scholar
[5]Du Mouchel, W., “The Pareto-optimality of an n-company reinsurance treatySkandinavsk Aktuarietidskrift, 51 (1968), pp. 165170.Google Scholar
[6]Lemaire, J., “A new concept of value for games without transferable utilitiesThe International Journal of Game Theory 1974.Google Scholar
[7]Lemaire, J., “Sur la valeur au sens de ShapleyCahiers du C.E.R.O. vol. 14, n° 1, 1974.Google Scholar
[8]Nash, J., “The Bargaining ProblemEconometrica, 18 (1950), pp. 155162.CrossRefGoogle Scholar
[9]Shapley, L. S., “A value for n-person gamesContributions to the theory of games, Vol. II. (Annals of Mathematics Studies, 28) pp. 307317.Google Scholar
[10]Shapley, L. S., “Utility comparison and the theory of gamesLa decision. Comptes rendus d'un colloque du C.N.R.S. à Aix-en-Provence. 1967, pp. 251263Google Scholar