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Optimal control for stochastic Volterra equations with multiplicative Lévy noise
- Publication Year :
- 2020
-
Abstract
- This paper is devoted to the analysis of an optimal control problem for stochastic integro-differential equations driven by a non-gaussian Levy 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.
- Subjects :
- Levy processes
Applied Mathematics
Weak solution
010102 general mathematics
Multiplicative function
Optimal control
01 natural sciences
Lévy process
Integro-differential Volterra equations
010104 statistics & probability
Noise
Stochastic differential equation
Complete monotone kernels
Monotone polygon
Time derivative
Applied mathematics
0101 mathematics
Analysis
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....652ce6824d01781941a28136f557b179