Stochastic Volterra equations with time-changed Lévy noise and maximum principles

Giulia Nunno () and Michele Giordano ()
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Giulia Nunno: University of Oslo
Michele Giordano: University of Oslo

Annals of Operations Research, 2024, vol. 336, issue 1, No 42, 1265-1287

Abstract: Abstract Motivated by a problem of optimal harvesting of natural resources, we study a control problem for Volterra type dynamics driven by time-changed Lévy 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 Di Nunno and Eide (Stoch Anal Appl 28:54-85, 2009). We prove both a sufficient and necessary stochastic maximum principle.

Keywords: Time-change; Conditionally independent increments; Backward stochastic Volterra integral equation; Maximum principle; Stochastic Volterra equations; Non-anticipating stochastic derivative; 60H10; 60H20; 93E20; 60G60; 91B70 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10479-023-05303-8

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