Existence of optimal controls for stochastic Volterra equations

Andrés Cárdenas, Sergio Pulido () and Rafael Serrano ()
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Andrés Cárdenas: Universidad del Rosario [Bogota]
Sergio Pulido: ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise, LaMME - Laboratoire de Mathématiques et Modélisation d'Evry - ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise - UEVE - Université d'Évry-Val-d'Essonne - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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Abstract: We provide sufficient conditions that guarantee the existence of relaxed optimal controls in the weak formulation of control problems for stochastic Volterra equations (SVEs). Our study can be applied to rough processes which arise when the kernel appearing in the controlled SVE is singular at zero. The proof of existence of relaxed optimal policies relies on the interaction between integrability hypotheses on the kernel, growth conditions on the running cost functional and on the coefficients of the controlled SVEs, and certain compactness properties of the class of Young measures on Suslin metrizable control sets. Under classical convexity assumptions, we also deduce the existence of optimal strict controls.

Keywords: stochastic Volterra equations; rough processes; relaxed control; Young measures; tightness; weak formulation (search for similar items in EconPapers)
Date: 2022-07-11
Note: View the original document on HAL open archive server: https://hal.science/hal-03720342v1
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Working Paper: Existence of optimal controls for stochastic Volterra equations (2024)
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