Existence of optimal controls for stochastic Volterra equations

Fuente: arXiv
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Main Authors: Cárdenas, Andrés, Pulido, Sergio, Serrano, Rafael
Format: Preprint
Published: 2022
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author Cárdenas, Andrés
Pulido, Sergio
Serrano, Rafael
author_facet Cárdenas, Andrés
Pulido, Sergio
Serrano, Rafael
contents We provide sufficient conditions that guarantee the existence of relaxed optimal controls in the weak formulation of stochastic control problems for stochastic Volterra equations (SVEs). Our study can be applied to rough processes that arise when the kernel appearing in the controlled SVE is singular at zero. The existence of relaxed optimal policies relies on the interaction between integrability hypotheses on the kernel and growth conditions on the running cost functional and the coefficients of the controlled SVEs. Under classical convexity assumptions, we can also deduce the existence of optimal strict controls.
format Preprint
id arxiv_https___arxiv_org_abs_2207_05169
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Existence of optimal controls for stochastic Volterra equations
Cárdenas, Andrés
Pulido, Sergio
Serrano, Rafael
Optimization and Control
Probability
Mathematical Finance
93E20, 60G22, 60H20
We provide sufficient conditions that guarantee the existence of relaxed optimal controls in the weak formulation of stochastic control problems for stochastic Volterra equations (SVEs). Our study can be applied to rough processes that arise when the kernel appearing in the controlled SVE is singular at zero. The existence of relaxed optimal policies relies on the interaction between integrability hypotheses on the kernel and growth conditions on the running cost functional and the coefficients of the controlled SVEs. Under classical convexity assumptions, we can also deduce the existence of optimal strict controls.
title Existence of optimal controls for stochastic Volterra equations
topic Optimization and Control
Probability
Mathematical Finance
93E20, 60G22, 60H20
url https://arxiv.org/abs/2207.05169