Ambrosino, Daniela; Fragnelli, Vito; Marina, Maria E. Resolving an insurance allocation problem: a procedural approach. (English) Zbl 1102.91063 Soc. Choice Welfare 26, No. 3, 625-643 (2006). Summary: 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 V. Fragnelli and M. E. Marina [Insur. Math. Econ. 33, No. 1, 75–85 (2003; Zbl 1025.62038)]. Cited in 1 Document MSC: 91B30 Risk theory, insurance (MSC2010) 91B32 Resource and cost allocation (including fair division, apportionment, etc.) Citations:Zbl 1025.62038 PDFBibTeX XMLCite \textit{D. Ambrosino} et al., Soc. Choice Welfare 26, No. 3, 625--643 (2006; Zbl 1102.91063) Full Text: DOI References: [1] Borch K (1974) The mathematical theory of insurance. Lexington Books, Lexington [2] Brams SJ, Taylor AD (1996) Fair-division. Cambridge University Press, New York [3] Brams SJ, Taylor AD (1999) The win-win solution. W.W.Norton & Company, London [4] Buhlmann H (1984) The general economic premium principle. Astin Bull 14:13–21 [5] Deprez O, Gerber HU (1985) On convex principles of premium calculation. Insur. Math Econ 4:179–189 · Zbl 0579.62090 [6] Fragnelli V, Marina ME (2003) A fair procedure in insurance. Insur. Math Econ 33:75–85 · Zbl 1025.62038 [7] 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 [8] Goovaerts MJ, De Vylder F, Haezendonck J (1984) Insurance premiums. North-Holland, Amsterdam · Zbl 0532.62082 [9] 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 · Zbl 1072.91590 [10] Knaster B (1946) Sur le Problème du Partage Pragmatique de H Steinhaus. Ann Soc Pol Mathematique 19:228–230 [11] Myerson RB (1991) Game theory: analysis of conflict. Harvard University Press, Cambridge · Zbl 0729.90092 [12] Nash JF (1950) The bargaining problem. Econometrica 21:155–162 · Zbl 1202.91122 [13] Raith MG (2000) Fair negotiation procedures. Math Soc Sci 39:303–322 · Zbl 0957.91004 [14] Steinhaus H (1948) The problem of fair division. Econometrica 16:101–104 [15] Suijs J, Borm P (1999) Stochastic cooperative games: superadditivity, convexity, and certainty equivalents. Games Econ Behav 27:331–345 · Zbl 0937.91020 [16] Thomson W (1994) Cooperative models of bargaining. In: Aumann RJ, Hart S (eds) Handbook of game theory, vol 2. Elsevier, Amsterdam, pp 1237–1284 · Zbl 0925.90084 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.