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Analysis of the Risk-Sharing Principal-Agent problem through the Reverse-Hölder inequality

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  • Jessica Martin

    (INSA Toulouse - Institut National des Sciences Appliquées - Toulouse - INSA - Institut National des Sciences Appliquées - UT - Université de Toulouse, IMT - Institut de Mathématiques de Toulouse UMR5219 - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INSA Toulouse - Institut National des Sciences Appliquées - Toulouse - INSA - Institut National des Sciences Appliquées - UT - Université de Toulouse - UT2J - Université Toulouse - Jean Jaurès - UT - Université de Toulouse - UT3 - Université Toulouse III - Paul Sabatier - UT - Université de Toulouse - CNRS - Centre National de la Recherche Scientifique)

  • Anthony Réveillac

    (INSA Toulouse - Institut National des Sciences Appliquées - Toulouse - INSA - Institut National des Sciences Appliquées - UT - Université de Toulouse, IMT - Institut de Mathématiques de Toulouse UMR5219 - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INSA Toulouse - Institut National des Sciences Appliquées - Toulouse - INSA - Institut National des Sciences Appliquées - UT - Université de Toulouse - UT2J - Université Toulouse - Jean Jaurès - UT - Université de Toulouse - UT3 - Université Toulouse III - Paul Sabatier - UT - Université de Toulouse - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this paper we provide an alternative framework to tackle the first-best Principal-Agent problem under CARA utilities. This framework leads to both a proof of existence and uniqueness of the solution to the Risk-Sharing problem under very general assumptions on the underlying contract space. Our analysis relies on an optimal decomposition of the expected utility of the Principal in terms of the reservation utility of the Agent and works both in a discrete time and continuous time setting. As a by-product this approach provides a novel way of characterizing the optimal contract in the CARA setting, which is as an alternative to the widely used Lagrangian method, and some analysis of the optimum.

Suggested Citation

  • Jessica Martin & Anthony Réveillac, 2019. "Analysis of the Risk-Sharing Principal-Agent problem through the Reverse-Hölder inequality," Working Papers hal-01874707, HAL.
    • Handle: RePEc:hal:wpaper:hal-01874707
    Note: View the original document on HAL open archive server: https://hal.science/hal-01874707v3
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    File URL: https://hal.science/hal-01874707v3/document
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    More about this item

    Keywords

    Uniqueness; Principal Agent problem; Existence; First-Best; Optimal Contracting Theory; Reverse Hölder inequality; Risk-Sharing; Borch rule;
    All these keywords.

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