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Backward stochastic Volterra integral equations with additive perturbations

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  • Djordjević, Jasmina
  • Janković, Svetlana

Abstract

The paper discusses a large class of stochastic Volterra integral equations whose coefficients additively depend on small perturbations. Their solutions are compared in the L2-sense with the solutions of the appropriate unperturbed equations of the equal or simpler type. More precisely, we prove for an arbitrary η > 0 that there exists an interval [t¯(η),T]⊂[0,T] on which the L2-difference between the solutions of the perturbed and unperturbed equations is less than η.

Suggested Citation

  • Djordjević, Jasmina & Janković, Svetlana, 2015. "Backward stochastic Volterra integral equations with additive perturbations," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 903-910.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:903-910
    DOI: 10.1016/j.amc.2015.05.077
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    References listed on IDEAS

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    1. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    2. Y. Ren, 2010. "On Solutions of Backward Stochastic Volterra Integral Equations with Jumps in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 144(2), pages 319-333, February.
    3. El-Karoui, N. & Hamadène, S., 2003. "BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 145-169, September.
    4. Yong, Jiongmin, 2006. "Backward stochastic Volterra integral equations and some related problems," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 779-795, May.
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    Cited by:

    1. Wang, Tianxiao & Yong, Jiongmin, 2019. "Backward stochastic Volterra integral equations—Representation of adapted solutions," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 4926-4964.
    2. Jasmina Djordjevic & Sanja Konjik & Darko Mitrović & Andrej Novak, 2021. "Global Controllability for Quasilinear Nonnegative Definite System of ODEs and SDEs," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 316-338, July.

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