Abstract
We consider risk sharing among individuals in a one-period setting under uncertainty that will result in payoffs to be shared among the members. We start with optimal risk sharing in an Arrow–Debreu economy, or equivalently, in a Borch-style reinsurance market. From the results of this model we can infer how risk is optimally distributed between individuals according to their preferences and initial endowments, under some idealized conditions. A main message in this theory is the mutuality principle, of interest related to the economic effects of pandemics. From this we point out some elements of a more general theory of syndicates, where in addition, a group of people are to make a common decision under uncertainty. We extend to a competitive market as a special case of such a syndicate.
Highlights
We analyze optimal risk sharing in society at large
A syndicate is defined to be a group of individuals who must make a common decision under uncertainty that will result in a payoff to be shared jointly among the members
When probability assessments are different between the members of the group, it is more difficult for the group to be a unanimous syndicate: All the members must have negative exponential utility functions, which is more limiting than having general Hyperbolic Absolute Risk Aversion (HARA) utility with the same cautiousness parameter
Summary
We analyze optimal risk sharing in society at large. We consider a one-period model of uncertainty where Pareto optimal risk sharing, or equivalently, optimal consumption is characterized. We present conditions under which the syndicate behaves as a Savage rational decision maker This was first treated in [1] as an extension of the general model by [2]. We review conditions under which any member of the syndicate can be relegated the task of making decisions under certainty on behalf of the group. This problem is considered both when the members of the group have homogeneous beliefs, and when the probabilities are heterogeneous. The paper ends with an application of the theory of syndicates to financial markets and general equilibrium
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