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

Author

Listed:
  • Giulia Nunno

    (University of Oslo
    NHH Norwegian School of Economics)

  • Michele Giordano

    (University of Oslo)

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.

Suggested Citation

  • Giulia Nunno & Michele Giordano, 2024. "Stochastic Volterra equations with time-changed Lévy noise and maximum principles," Annals of Operations Research, Springer, vol. 336(1), pages 1265-1287, May.
    • Handle: RePEc:spr:annopr:v:336:y:2024:i:1:d:10.1007_s10479-023-05303-8
    DOI: 10.1007/s10479-023-05303-8
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