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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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    References listed on IDEAS

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    1. Jan-Frederik Mai & Matthias Scherer, 2009. "A Tractable Multivariate Default Model Based On A Stochastic Time-Change," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 227-249.
    2. Anton O. Belyakov & Vladimir M. Veliov, 2016. "On Optimal Harvesting in Age-Structured Populations," Dynamic Modeling and Econometrics in Economics and Finance, in: Herbert Dawid & Karl F. Doerner & Gustav Feichtinger & Peter M. Kort & Andrea Seidl (ed.), Dynamic Perspectives on Managerial Decision Making, pages 149-166, Springer.
    3. Bernt øksendal & Tusheng Zhang, 2010. "Optimal Control with Partial Information for Stochastic Volterra Equations," International Journal of Stochastic Analysis, Hindawi, vol. 2010, pages 1-25, June.
    4. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    5. Nacira Agram & Bernt Øksendal, 2015. "Malliavin Calculus and Optimal Control of Stochastic Volterra Equations," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 1070-1094, December.
    6. Borovkova, Svetlana & Schmeck, Maren Diane, 2017. "Electricity price modeling with stochastic time change," Energy Economics, Elsevier, vol. 63(C), pages 51-65.
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