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arXiv · 2011.07341

Stochastic Volterra equations with time-changed L\'evy noise and maximum principles

Giulia di Nunno·Michele Giordano
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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.

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Giulia di Nunno, Michele Giordano. 2020-11-14. Stochastic Volterra equations with time-changed L\'evy noise and maximum principles. https://arxiv.org/abs/2011.07341

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