Linear versus Nonlinear Allocation Rules in Risk Sharing Under Financial Fairness
32 Pages Posted: 5 Jan 2017 Last revised: 5 Aug 2018
Date Written: May 21, 2018
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: Suggested Citation