Existence of optimal controls for stochastic Volterra equations
| Autor: | Cárdenas, Andrés, Pulido, Sergio, Serrano, Rafael |
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| Přispěvatelé: | Universidad del Rosario [Bogota], Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Andrés Cárdenas and Rafael Serrano thank Alianza EFI-Colombia Cientifica grant, codes 60185 and FP44842-220-2018 for financial support., The research of the Sergio Pulido benefited from the financial support of the chairs 'Deep finance & Statistics' and 'Machine Learning & systematic methods in finance' of École Polytechnique., Sergio Pulido acknowledges support by the Europlace Institute of Finance (EIF) and the Labex Louis Bachelier, research project: 'The impact of information on financial markets'. |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
relaxed control
weak formulation [QFIN]Quantitative Finance [q-fin] Probability (math.PR) 93E20 60G22 60H20 rough processes tightness Mathematical Finance (q-fin.MF) [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] FOS: Economics and business Optimization and Control (math.OC) Quantitative Finance - Mathematical Finance stochastic Volterra equations Young measures FOS: Mathematics [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] MSC2010 classifications: 93E20 60G22 60H20 Mathematics - Optimization and Control Mathematics - Probability |
| Popis: | 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. 30 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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