Linear versus Nonlinear Allocation Rules in Risk Sharing Under Financial Fairness

32 Pages Posted: 5 Jan 2017 Last revised: 5 Aug 2018

See all articles by J. M. Schumacher

J. M. Schumacher

University of Amsterdam - Department of Quantitative Economics (KE)

Date Written: May 21, 2018

Abstract

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 holds for all participants, then the exchange is said to be "financially fair." It has been shown by Buehlmann 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. We compare the performance of the linear rule to that of the general (nonlinear) rule in a number of specific cases.

Keywords: risk exchange, Pareto efficiency, financial fairness, cooperative investment

JEL Classification: G22, D86

Suggested Citation

Schumacher, J.M. (Hans), Linear versus Nonlinear Allocation Rules in Risk Sharing Under Financial Fairness (May 21, 2018). Available at SSRN: https://ssrn.com/abstract=2892760 or http://dx.doi.org/10.2139/ssrn.2892760

J.M. (Hans) Schumacher (Contact Author)

University of Amsterdam - Department of Quantitative Economics (KE) ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

Register to save articles to
your library

Register

Paper statistics

Downloads
77
Abstract Views
437
rank
312,157
PlumX Metrics