Stochastic Volterra equations with time-changed L\'evy noise and maximum principles
Probability
2023-03-07 v6 Optimization and Control
Abstract
Motivated by a problem of optimal harvesting of natural resources, we study a control problem for Volterra type dynamics driven by time-changed L\'evy noises, which are in general not Markovian. To exploit the nature of the noise, we make use of different kind of information flows within a maximum principle approach. For this we work with backward stochastic differential equations (BSDE) with time-change and exploit the non-anticipating stochastic derivative introduced in [15]. We prove both a sufficient and necessary stochastic maximum principle.
Cite
@article{arxiv.2011.07341,
title = {Stochastic Volterra equations with time-changed L\'evy noise and maximum principles},
author = {Giulia di Nunno and Michele Giordano},
journal= {arXiv preprint arXiv:2011.07341},
year = {2023}
}