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Integral Operator Riccati Equations Arising in Stochastic Volterra Control Problems

Author

Listed:
  • Eduardo Abi Jaber

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, UP1 UFR27 - Université Paris 1 Panthéon-Sorbonne - UFR Mathématiques & Informatique - UP1 - Université Paris 1 Panthéon-Sorbonne)

  • Enzo Miller

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité)

  • Huyen Pham

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité)

Abstract

We establish existence and uniqueness for infinite-dimensional Riccati equations taking values in the Banach space $L^1(\mu \otimes \mu)$ for certain signed matrix measures $\mu$ which are not necessarily finite. Such equations can be seen as the infinite-dimensional analogue of matrix Riccati equations, and they appear in the linear-quadratic control theory of stochastic Volterra equations.

Suggested Citation

  • Eduardo Abi Jaber & Enzo Miller & Huyen Pham, 2021. "Integral Operator Riccati Equations Arising in Stochastic Volterra Control Problems," Post-Print hal-03264893, HAL.
    • Handle: RePEc:hal:journl:hal-03264893
    DOI: 10.1137/19M1298287
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    Cited by:

    1. Eduardo Abi Jaber, 2022. "The Laplace transform of the integrated Volterra Wishart process," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 309-348, January.
    2. Eduardo Abi Jaber & Eyal Neuman, 2022. "Optimal Liquidation with Signals: the General Propagator Case," Working Papers hal-03835948, HAL.
    3. Eduardo Abi Jaber & Eyal Neuman, 2022. "Optimal Liquidation with Signals: the General Propagator Case," Papers 2211.00447, arXiv.org.

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