In this paper, we study a class of optimal control problems for stochastic Volterra equations in infinite dimensions. We are concerned with a class of stochastic Volterra integrodifferential problem with completely monotone kernels, where we assume that the noise enters the system when we introduce a control. We provide a semigroup setting for the problem, by the state space setting; the applications to optimal control provide other interesting results and require a precise description of the properties of the generated semigroup. In our stochastic optimal control problems, the drift term of the equation has a linear growth in the control variable, the cost functional has a quadratic growth, and the control process belongs to the class of square integrable, adapted processes with no bound assumed on it. Our main results are the existence for the optimal feedback control, the identification of the optimal cost with the value Y0 of the maximal solution (Y,Z) of the backward stochastic differential equation, the existence of a weak solution to the so-called closed loop equation and, finally, the construction of an optimal feedback in terms of the process Z. © 2012 Society for Industrial and Applied Mathematics.

Bonaccorsi, S., Confortola, F., Mastrogiacomo, E. (2012). Optimal Control for Stochastic Volterra Equations with Completely Monotone Kernels. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 50, 748-789 [10.1137/100782875].

Optimal Control for Stochastic Volterra Equations with Completely Monotone Kernels

MASTROGIACOMO, ELISA
2012

Abstract

In this paper, we study a class of optimal control problems for stochastic Volterra equations in infinite dimensions. We are concerned with a class of stochastic Volterra integrodifferential problem with completely monotone kernels, where we assume that the noise enters the system when we introduce a control. We provide a semigroup setting for the problem, by the state space setting; the applications to optimal control provide other interesting results and require a precise description of the properties of the generated semigroup. In our stochastic optimal control problems, the drift term of the equation has a linear growth in the control variable, the cost functional has a quadratic growth, and the control process belongs to the class of square integrable, adapted processes with no bound assumed on it. Our main results are the existence for the optimal feedback control, the identification of the optimal cost with the value Y0 of the maximal solution (Y,Z) of the backward stochastic differential equation, the existence of a weak solution to the so-called closed loop equation and, finally, the construction of an optimal feedback in terms of the process Z. © 2012 Society for Industrial and Applied Mathematics.
Articolo in rivista - Articolo scientifico
Stochastic differential equations in infinite dimensions, dynamical bound- ary conditions, optimal control
English
2012
50
748
789
none
Bonaccorsi, S., Confortola, F., Mastrogiacomo, E. (2012). Optimal Control for Stochastic Volterra Equations with Completely Monotone Kernels. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 50, 748-789 [10.1137/100782875].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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: https://hdl.handle.net/10281/48438
Citazioni
  • Scopus 16
  • ???jsp.display-item.citation.isi??? 16
Social impact