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Backward stochastic Volterra integral equations—Representation of adapted solutions

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  • Wang, Tianxiao
  • Yong, Jiongmin

Abstract

For backward stochastic Volterra integral equations (BSVIEs, for short), under some mild conditions, the so-called adapted solutions or adapted M-solutions uniquely exist. However, satisfactory regularity of the solutions is difficult to obtain in general. Inspired by the decoupling idea of forward–backward stochastic differential equations, in this paper, for a class of BSVIEs, a representation of adapted M-solutions is established by means of the so-called representation partial differential equations and (forward) stochastic differential equations. Well-posedness of the representation partial differential equations are also proved in certain sense.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:12:p:4926-4964
    DOI: 10.1016/j.spa.2018.12.016
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    References listed on IDEAS

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    1. Wang, Tianxiao & Yong, Jiongmin, 2015. "Comparison theorems for some backward stochastic Volterra integral equations," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 1756-1798.
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    6. Camilo Hern'andez & Dylan Possamai, 2023. "Time-inconsistent contract theory," Papers 2303.01601, arXiv.org.

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