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An ergodic BSDE approach to entropic risk measure and its large time behavior

Author

Listed:
  • Wing Fung Chong

    (King‘s College London)

  • Ying Hu

    (IRMAR - Institut de Recherche Mathématique de Rennes - UR - Université de Rennes - INSA Rennes - Institut National des Sciences Appliquées - Rennes - INSA - Institut National des Sciences Appliquées - ENS Rennes - École normale supérieure - Rennes - UR2 - Université de Rennes 2 - CNRS - Centre National de la Recherche Scientifique - INSTITUT AGRO Agrocampus Ouest - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement)

  • Gechun Liang

    (King‘s College London)

  • Thaleia Zariphopoulou

    (University of Texas at Austin [Austin])

Abstract

This paper shows that the long-time behavior of the entropic risk measure (under both forward performance process framework and classical utility framework) converges to a constant, which is independent of the initial state of the stochastic factors in a stochastic factor model. The exponential convergence rate to the long-term limit is also obtained by using ergodic backward stochastic differential equation method. Finally, the paper establishes a connection between the two notions of entropic risk measures and their large time behavior.

Suggested Citation

  • Wing Fung Chong & Ying Hu & Gechun Liang & Thaleia Zariphopoulou, 2019. "An ergodic BSDE approach to entropic risk measure and its large time behavior," Post-Print hal-01361585, HAL.
    • Handle: RePEc:hal:journl:hal-01361585
    DOI: 10.1007/s00780-018-0377-3
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    Cited by:

    1. Xue Dong He & Moris S. Strub & Thaleia Zariphopoulou, 2021. "Forward rank‐dependent performance criteria: Time‐consistent investment under probability distortion," Mathematical Finance, Wiley Blackwell, vol. 31(2), pages 683-721, April.
    2. Goncalo dos Reis & Vadim Platonov, 2020. "Forward utilities and Mean-field games under relative performance concerns," Papers 2005.09461, arXiv.org, revised Sep 2020.

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