Optimal control for stochastic Volterra equations with multiplicative Lévy noise

被引：0
作者：
Stefano Bonaccorsi
Fulvia Confortola
机构：
[1] Università di Trento,Dipartimento di Matematica
[2] Politecnico di Milano,Dipartimento di Matematica F. Brioschi
来源：
Nonlinear Differential Equations and Applications NoDEA | 2020年 / 27卷
关键词：
Optimal control; Integro-differential Volterra equations; Complete monotone kernels; Lévy processes; Primary 45K05; Secondary 60H30; 93E20;
D O I：
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学科分类号：
摘要：
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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  • [1] Albeverio S(2009)Existence of mild solutions for stochastic differential equations and semilinear equations with non-gaussian Lévy noise Stoch. Process. Appl. 119 835-863
  • [2] Mandrekar V(2002)Dynamic models of long-memory processes driven by Lévy noise J. Appl. Probab. 39 730-747
  • [3] Rüdiger B(2017)Optimal control of semi-Markov processes with a backward stochastic differential equations approach Math. Control Signals Syst. 29 35-83
  • [4] Anh VV(1997)Backward stochastic differential equations and integral-partial differential equations Stoch. Stoch. Rep. 60 57-404
  • [5] Heyde CC(1973)Conjugate convex functions in optimal stochastic control J. Math. Anal. Appl. 44 384-1061
  • [6] Leonenko NN(1975)Martingales on jump processes, Part I: pepresentation results. Part II: applications SIAM J. Control 13 999-339
  • [7] Bandini E(2009)An analytic approach to stochastic Volterra equations with completely monotone kernels J. Evol. Equ. 9 315-789
  • [8] Confortola F(2012)Optimal control for stochastic Volterra equations with completely monotone kernels SIAM J. Control Optim. 50 748-1587
  • [9] Barles G(2012)Asymptotic behavior of a class of nonlinear stochastic heat equations with memory effects SIAM J. Math. Anal. 44 1562-594
  • [10] Buckdahn R(2013)Volterra equations in Banach spaces with completely monotone kernels NoDEA Nonlinear Differ. Equ. Appl. 20 557-314
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