In this paper we are concerned with a class of stochastic Volterra integro-dierential problems with completely monotone kernels, where we assume that the noise enters the system when we introduce a control. We start by reformulating the state equation into a semilinear evolution equation which can be treated by semigroup methods. The application to optimal control provide other interesting result and require a precise descriprion of the properties of the generated semigroup. The rst main result of the paper is the proof of existence and uniqueness of a mild solution for the corresponding Hamilton-Jacobi-Bellman (HJB) equation. The main technical point consists in the dierentiability of the BSDE associated with the reformulated equation with respect to its initial datum x.

Feedback optimal control for stochastic Volterra equations with completely monotone kernels.

CONFORTOLA, FULVIA;
2015

Abstract

In this paper we are concerned with a class of stochastic Volterra integro-dierential problems with completely monotone kernels, where we assume that the noise enters the system when we introduce a control. We start by reformulating the state equation into a semilinear evolution equation which can be treated by semigroup methods. The application to optimal control provide other interesting result and require a precise descriprion of the properties of the generated semigroup. The rst main result of the paper is the proof of existence and uniqueness of a mild solution for the corresponding Hamilton-Jacobi-Bellman (HJB) equation. The main technical point consists in the dierentiability of the BSDE associated with the reformulated equation with respect to its initial datum x.
Stochastic Volterra integral equation, backward stochastic differential equations, optimal control, HJB equation, feedback law.
File in questo prodotto:
File Dimensione Formato  
Feedback Optimalcontr Volterra eq compl-monotone-kernel .pdf

accesso aperto

Descrizione: Articolo principale
: Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione 686.09 kB
Formato Adobe PDF
686.09 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/622165.14
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact