Abstract
In this paper we study the problem of the determination of a fair allocation in a co-insurance problem, i.e., how some insurance companies have to share the risk and the premium. We develop two procedures that produce a proportional and an equitable allocation, respectively. The procedures are applied to a real situation arising from environmental risk and the resulting allocations are compared with the classical quota share allocation and with an envy-free allocation resulting from a procedure presented in Fragnelli and Marina (Insur. Math Econ 33:75–85, 2003).
Similar content being viewed by others
References
Borch K (1974) The mathematical theory of insurance. Lexington Books, Lexington
Brams SJ, Taylor AD (1996) Fair-division. Cambridge University Press, New York
Brams SJ, Taylor AD (1999) The win-win solution. W.W.Norton & Company, London
Buhlmann H (1984) The general economic premium principle. Astin Bull 14:13–21
Deprez O, Gerber HU (1985) On convex principles of premium calculation. Insur. Math Econ 4:179–189
Fragnelli V, Marina ME (2003) A fair procedure in insurance. Insur. Math Econ 33:75–85
Fragnelli V, Marina ME (2004) Co-insurance games and environmental pollution risk. In: Carraro C, Fragnelli V (eds) Game practice and the environment. Edward Elgar Publishing, Cheltenham, pp 145–163
Goovaerts MJ, De Vylder F, Haezendonck J (1984) Insurance premiums. North-Holland, Amsterdam
Haake CJ, Raith MG, Su FE (2002) Bidding for envy-freeness: a procedural approach to n-player fair-division problems. Soc Choice Welfare 19:723–749
Knaster B (1946) Sur le Problème du Partage Pragmatique de H Steinhaus. Ann Soc Pol Mathematique 19:228–230
Myerson RB (1991) Game theory: analysis of conflict. Harvard University Press, Cambridge
Nash JF (1950) The bargaining problem. Econometrica 21:155–162
Raith MG (2000) Fair negotiation procedures. Math Soc Sci 39:303–322
Steinhaus H (1948) The problem of fair division. Econometrica 16:101–104
Suijs J, Borm P (1999) Stochastic cooperative games: superadditivity, convexity, and certainty equivalents. Games Econ Behav 27:331–345
Thomson W (1994) Cooperative models of bargaining. In: Aumann RJ, Hart S (eds) Handbook of game theory, vol 2. Elsevier, Amsterdam, pp 1237–1284
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ambrosino, D., Fragnelli, V. & Marina, M.E. Resolving an Insurance Allocation Problem: A Procedural Approach. Soc Choice Welfare 26, 625–643 (2006). https://doi.org/10.1007/s00355-006-0108-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00355-006-0108-0