This paper is devoted to the analysis of an optimal control problem for stochastic integro-differential equations driven by a non-gaussian Lévy noise. The memory effect in the equation is driven by a completely monotone kernel (thus covering, for instance, the class of fractional time derivative of order less than 1). We suppose that the control acts on the jump rate of the noise. We show that this allows to tackle the problem through a backward stochastic differential equations approach, since the structure condition required by this approach is naturally satisfied. We solve the optimal control problem of minimizing a cost functional on a finite time horizon, with both running and final costs. We finally prove the existence of a weak solution of the closed-loop equation and we construct an optimal feedback control.

Optimal control for stochastic Volterra equations with multiplicative Lévy noise / Bonaccorsi, Stefano; Confortola, Fulvia. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - STAMPA. - 2020, 27:3(2020), pp. 26.1-26.26. [10.1007/s00030-020-00631-1]

Optimal control for stochastic Volterra equations with multiplicative Lévy noise

Bonaccorsi, Stefano;Confortola, Fulvia
2020

Abstract

This paper is devoted to the analysis of an optimal control problem for stochastic integro-differential equations driven by a non-gaussian Lévy noise. The memory effect in the equation is driven by a completely monotone kernel (thus covering, for instance, the class of fractional time derivative of order less than 1). We suppose that the control acts on the jump rate of the noise. We show that this allows to tackle the problem through a backward stochastic differential equations approach, since the structure condition required by this approach is naturally satisfied. We solve the optimal control problem of minimizing a cost functional on a finite time horizon, with both running and final costs. We finally prove the existence of a weak solution of the closed-loop equation and we construct an optimal feedback control.
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Bonaccorsi, Stefano; Confortola, Fulvia
Optimal control for stochastic Volterra equations with multiplicative Lévy noise / Bonaccorsi, Stefano; Confortola, Fulvia. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - STAMPA. - 2020, 27:3(2020), pp. 26.1-26.26. [10.1007/s00030-020-00631-1]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/295203
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