Participation in risk sharing under ambiguity
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Participation in risk sharing under ambiguity Jan Werner1 Accepted: 26 October 2020 Ó Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper is about (non) participation in efficient risk sharing among agents who have ambiguous beliefs about uncertain states of nature. The question we ask is whether and how can ambiguous beliefs give rise to some agents not participating in efficient risk sharing. Ambiguity of beliefs is described by the multiple-prior expected utility of Gilboa and Schmeidler (J Math Econ 18:141–153, 1989), or the variational preferences of Maccheroni et al. (Econometrica 74(6):1447–1498, 2006). The main result says that if the aggregate risk is relatively small, then the agents whose beliefs are the most ambiguous do not participate in risk sharing. The higher the ambiguity of those agents’ beliefs, the more likely is their non-participation. Another factor making non-participation more likely is low risk aversion of agents whose beliefs are less ambiguous. We discuss implications of our results on agents’ participation in trade in equilibrium in assets markets. Keywords Risk sharing Ambiguity aversion Pareto efficiency
1 Introduction Expected utility hypothesis together with (strict) risk aversion and common probabilities have strong implications on efficient risk sharing among multiple agents. First, agents’ consumption plans are comonotone with aggregate resources. Second, every agent participates in risk sharing by holding at least a small fraction of the aggregate risk. These results are at odds with empirical observations. Individual consumption often deviates from positive correlation with the aggregate consumption.1 A large fraction of population in the US is not participating in asset markets thereby abstaining from sharing the aggregate financial risk. Ambiguity of beliefs has been suggested as a way to reconcile the differences between the observed patterns and the rules of efficient risk sharing. Two closely 1
Positive correlation is implied by comonotonicity, see LeRoy and Werner (2014, pg. 158).
& Jan Werner [email protected] 1
Department of Economics, University of Minnesota, Minneapolis, MN 55455, USA
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J. Werner
related, standard models of decision making with ambiguous beliefs are the multipleprior expected utility of Gilboa and Schmeidler (1989) and the variational preferences of Maccheroni et al. (2006). Under the multiple-prior expected utility hypothesis, an agent has a set of probability measures (or priors) as her beliefs and evaluates an uncertain prospect by taking the minimum of expected utilities over the set of beliefs. One of the main implications of the multiple-prior model is the possibility of nonparticipation in trade. A simple illustration of this is the portfolio inertia of Dow and Werlang (1992). An agent with multiple-prior expected utility and risk-free initial wealth does not invest in a risky asset for a range prices. As long as the expected return on the risky asset u
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