Finance and Stochastics

, Volume 22, Issue 2, pp 443–502 | Cite as

Stability of Radner equilibria with respect to small frictions

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Abstract

We study risk-sharing equilibria with trading subject to small proportional transaction costs. We show that the frictionless equilibrium prices also form an “asymptotic equilibrium” in the small-cost limit. More precisely, there exist asymptotically optimal policies for all agents and a split of the trading cost according to their risk aversions for which the frictionless equilibrium prices still clear the market. Starting from a frictionless equilibrium, this allows studying the interplay of volatility, liquidity and trading volume.

Keywords

Trading costs Radner equilibrium Asymptotics Stability Transaction tax 

Mathematics Subject Classification (2010)

91B51 91G10 

JEL Classification

D52 G11 G12 

Notes

Acknowledgements

The authors are grateful to Peter Bank, Rama Cont, Paolo Guasoni, Jan Kallsen, Kasper Larsen, Rémy Praz and Steven E. Shreve for fruitful discussions and to Michail Anthropelos and Sebastian Herrmann for a careful reading of an earlier version. Moreover, they sincerely thank two anonymous referees for their insightful and detailed remarks. The first author was partially supported by the Swiss National Science Foundation (SNF) under grant 150101. Parts of this paper were written while the second author was visiting ETH Zürich; he is grateful to the Forschungsinstitut für Mathematik and H.M. Soner for their hospitality.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of WarwickCoventryUK
  2. 2.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA

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