Integral Operator Riccati Equations Arising in Stochastic Volterra Control Problems

Eduardo Abi Jaber (), Enzo Miller and Huyen Pham
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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

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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.

Keywords: infinite-dimensional Lyapunov equation; integral operator Riccati equation; linear-quadratic control; stochastic Volterra equations (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (4)

Published in SIAM Journal on Control and Optimization, 2021, 59 (2), pp.1581-1603. ⟨10.1137/19M1298287⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03264893

DOI: 10.1137/19M1298287

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