Large Risks, Limited Liability, and Dynamic Moral Hazard

Authors

  • Bruno Biais,

    1. Toulouse School of Economics (CNRS, GREMAQ, IDEI), Université Toulouse 1, 21 Allée de Brienne, 31000 Toulouse, France; biais@cict.fr
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  • Thomas Mariotti,

    1. Toulouse School of Economics (CNRS, GREMAQ, IDEI), Université Toulouse 1, 21 Allée de Brienne, 31000 Toulouse, France; mariotti@cict.fr
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  • Jean-Charles Rochet,

    1. Toulouse School of Economics (GREMAQ, IDEI), Université Toulouse 1, 21 Allée de Brienne, 31000 Toulouse, France; rochet@cict.fr
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  • Stéphane Villeneuve

    1. Toulouse School of Economics (CRM, IDEI), Université Toulouse 1, 21 Allée de Brienne, 31000 Toulouse, France; stephane.villeneuve@univ-tlse1.fr
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    • We thank a co-editor, and three anonymous referees for very thoughtful and detailed comments. We also thank Ron Anderson, Dirk Bergemann, Peter DeMarzo, Ivar Ekeland, Eduardo Faingold, Michael Fishman, Jean-Pierre Florens, Xavier Gabaix, Christian Gollier, Alexander Gümbel, Zhiguo He, Christian Hellwig, Augustin Landier, Ali Lazrak, Erzo Luttmer, George Mailath, Roger Myerson, Thomas Philippon, Bernard Salanié, Yuliy Sannikov, Hyun Song Shin, Dimitri Vayanos, Nicolas Vieille, and Wei Xiong for very valuable feedback. Finally, we thank seminar audiences at Imperial College London, New York University, Oxford-Man Institute of Quantitative Finance, Princeton University, Universidad Carlos III de Madrid, Université Paris 1, Universiteit van Tilburg, University College London, University of Edinburgh, University of Warwick, Wissenschaftszentrum Berlin für Sozialforschung, and Yale University, as well as conference participants at the 2007 CEPR Corporate Finance and Risk Management Conference, the 2007 IDEI–LERNA Conference on Environment and Resource Economics, the 2007 Oxford Finance Summer Symposium, the 2008 Cowles Summer Conference, the 2008 Pacific Institute for the Mathematical Sciences Summer School in Finance, the 2009 Institut Finance Dauphine Workshop on Dynamic Risk Sharing, and the 2009 Paul Woolley Centre for Capital Market Dysfunctionality Conference for many useful discussions. Financial support from the Chaire Finance Durable et Investissement Responsable, the Chaire Marchés des Risques et Création de Valeur, the ERC Starting Grant 203929-ACAP, the Europlace Institute of Finance, and the Fédération Française des Sociétés d'Assurances is gratefully acknowledged.


Abstract

We study a continuous-time principal–agent model in which a risk-neutral agent with limited liability must exert unobservable effort to reduce the likelihood of large but relatively infrequent losses. Firm size can be decreased at no cost or increased subject to adjustment costs. In the optimal contract, investment takes place only if a long enough period of time elapses with no losses occurring. Then, if good performance continues, the agent is paid. As soon as a loss occurs, payments to the agent are suspended, and so is investment if further losses occur. Accumulated bad performance leads to downsizing. We derive explicit formulae for the dynamics of firm size and its asymptotic growth rate, and we provide conditions under which firm size eventually goes to zero or grows without bounds.

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