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LINEAR VERSUS NONLINEAR ALLOCATION RULES IN RISK SHARING UNDER FINANCIAL FAIRNESS

Published online by Cambridge University Press:  06 August 2018

Johannes M. Schumacher
Johannes M. Schumacher*
Affiliation:
University of Amsterdam, Faculty of Economics and Business, Section Quantitative Economics, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands
*
E-Mail: [email protected]
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Abstract

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In a risk exchange, participants trade a privately owned risk for a share in a pool. If participants agree on a valuation rule, it can be decided whether or not, according to the given rule, these trades take place at equal value. If equality of values holds for all participants, then the exchange is said to be “financially fair”. It has been shown by Bühlmann and Jewell (1979) that, under mild assumptions, the constraint of financial fairness singles out a unique solution among the set of all Pareto efficient risk exchanges. In this paper, we find that an analogous statement is true if we limit ourselves to linear exchanges. Conditions are provided for existence and uniqueness of linear sharing rules that are both financially fair and Pareto efficient among all linear sharing rules. The performance of the linear rule is compared to that of the general (nonlinear) rule in a number of specific cases.

Keywords

Risk sharingallocation rulesfinancial fairnessBorch theoremsyndicates
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 3 , September 2018 , pp. 995 - 1024
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © Astin Bulletin 2018

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