Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-12-01T00:08:24.005Z Has data issue: false hasContentIssue false
  • English
  • Français

Existence and Uniqueness of Equilibrium in a Reinsurance Syndicate

Published online by Cambridge University Press:  09 August 2013

Knut K. Aase
Knut K. Aase*
Affiliation:
Norwegian School of Economics and Business Administration, 5045 Bergen, Norway, and Centre of Mathematics for Applications (CMA), University of Oslo, Norway, E-Mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we consider a reinsurance syndicate, assuming that Pareto optimal allocations exist. Under a continuity assumption on preferences, we show that a competitive equilibrium exists and is unique. Our conditions allow for risks that are not bounded, and we show that the most standard models satisfy our set of sufficient conditions, which are thus not restrictive. Our approach is to transform the analysis from an infinite dimensional to a finite dimensional setting.

Keywords

Existence of equilibriumuniqueness of equilibriumPareto optimalityreinsurance modelsyndicate theoryrisk toleranceexchange economyprobability distributionsWalras' law
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 2 , November 2010 , pp. 491 - 517
Copyright
Copyright © International Actuarial Association 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aase, K.K. (1993) “Equilibrium in a Reinsurance Syndicate; Existence, Uniqueness and Characterization”. ASTIN Bulletin 22(2), 185–211.Google Scholar
Aase, K.K. (2002) “Perspectives of Risk Sharing”. Scand. Actuarial J. 2, 73–128.CrossRefGoogle Scholar
Aase, K.K. (2009) “The Nash bargaining solution vs. equilibrium in a reinsurance syndicate”. Scand. Actuarial J. 3, 219–238.Google Scholar
Araujo, A.P. (1987) “The non-existence of smooth demand in general Banach spaces”. Journal of Mathematical Economics 17, 1–11.Google Scholar
Araujo, A.P. and Monteiro, P.K. (1989) “Equilibrium without uniform conditions”. Journal of Economic Theory, 48(2), 416–427.Google Scholar
Arrow, K.J. (1953) “Le role des valeurs boursiers pour la répartition la meilleure des risques”. Colloques Internationaux du CNRS, XLL, Paris, 41–88.Google Scholar
Arrow, K.J. and Hahn, F.H. (1971) General Competitive Analysis. Holden-Day, Inc, San Francisco; Oliver & Boyd, Edinburgh.Google Scholar
Bewley, T. (1969) “A theorem on the existence of competitive equilibria in a market with a finite number of agents and whose commodity space is L∞ ”. CORE Discussion Paper, Université de Louvain.Google Scholar
Bewley, T. (1972) “Existence of equilibria in economies with ini nitely many commodities”. Journal of Economic Theory 4, 514–540.Google Scholar
Borch, K.H. (1960) “The safety loading of reinsurance premiums”. Skandinavisk Aktuarietidsskrift 163–184.Google Scholar
Borch, K.H. (1962) “Equilibrium in a reinsurance market”. Econometrica 30, 424–444.Google Scholar
Borch, K.H. (1985) “A theory of insurance premiums”. The Geneva Papers on Risk and Insurance Theory 10; 192–208.Google Scholar
Bühlmann, H. (1980) “An economic premium principle”. ASTIN Bulletin 11, 52–60.Google Scholar
Bühlmann, H. (1984) “The general economic premium principle”. ASTIN Bulletin 14, 13–21.Google Scholar
Dana, R.-A. (1993) “Existence and uniqueness of equilibria when preferences are additively separable”. Econometrica 61(4), 953–958.Google Scholar
DuMouchel, W.H. (1968) “The Pareto optimality of an n-company reinsurance treaty”. Skandinavisk Aktuarietidsskrift 165–170.Google Scholar
Gerber, H.U. (1978) “Pareto-optimal risk exchanges and related decision problems”. ASTIN Bulletin 10, 25–33.Google Scholar
Magill, M. (1981) “An equilibrium existence theorem”. Journal of Mathematical Analysis and Applications 84, 162–169.CrossRefGoogle Scholar
Mas-Colell, A. (1986) “The price equilibrium existence problem in topological vector lattices”. Econometrica 54, 1039–1054.Google Scholar
Mas-Colell, A. and Zame, W.R. (1991) “Equilibrium theory in ini nite dimensional spaces”. In Handbook of Mathematical Economics Vol. IV, Ch. 34, pp. 1835–1898. (Edited by Hildenbrand, W. and Sonnenschein, H..) Elsevier Science Publishers B.V. Google Scholar
Negishi, T. (1960) “Welfare Economics and existence of an equilibrium for a competitive economy”. Metroeconomica 12, 92–97.Google Scholar
Wilson, R. (1968) “The theory of syndicates”. Econometrica 36(1), 119–132.Google Scholar