On the fragility of mutual insurance arrangements

37 Pages Posted: 20 Mar 2021 Last revised: 10 May 2022

See all articles by Delia Coculescu

Delia Coculescu

University of Zurich - Department of Banking and Finance

Oana Lupascu-Stamate

affiliation not provided to SSRN

Gabriele Visentin

University of Zurich - Institute of Mathematics

Date Written: January 4, 2021

Abstract

Mutual insurance is a means of managing idiosyncratic liquidity shocks by cooperation in groups, where shortages of group members are covered by the existing surpluses of other members (i.e., by borrowing and lending relations).
Interbank lending may be considered as such a mechanism of mutual insurance.

It is often believed that idiosyncratic shocks may be better managed in larger groups. This paper shows that this is not always the case, even as we only consider homogeneous groups and independent liquidity shocks.

Using a continuous time stochastic game, we explore essential questions regarding mutual insurance: what are the characteristics of populations where cooperation is valuable, versus individualist populations, where cooperation destroys value; how large should be the groups of cooperating entities? We also measure the inefficiencies of the Nash equilibria, arising from strategic cooperation, as compared with optimal cooperation.

Our results show in the space of the parameters the existence of fragility zones, where small shifts in the parameters of the model, lead to critical changes in the levels of cooperation in equilibrium: from infinite to none. This points to an intrinsic fragility of mutual insurance that has not been emphasised in the literature so far. In practice, the results are helpful in shedding additional light on the reasons why the interbank lending markets are sometimes subject to sudden stops, hence complementing a vast literature on the topic.

Keywords: systemic risk, risk sharing, insurance, stochastic games in continuous time, inefficiencies of Nash equilibria, interbank lending.

JEL Classification: C72,C73

Suggested Citation

Coculescu, Delia and Lupascu-Stamate, Oana and Visentin, Gabriele, On the fragility of mutual insurance arrangements (January 4, 2021). Available at SSRN: https://ssrn.com/abstract=1189182 or http://dx.doi.org/10.2139/ssrn.1189182

Delia Coculescu (Contact Author)

University of Zurich - Department of Banking and Finance ( email )

Schönberggasse 1
Zürich, 8001
Switzerland

Oana Lupascu-Stamate

affiliation not provided to SSRN

Gabriele Visentin

University of Zurich - Institute of Mathematics ( email )

Switzerland

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