Backward Stochastic Volterra Integral Equations--- Representation of Adapted Solutions

Tianxiao Wang; Jiongmin Yong

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arXiv · 1802.03659

Backward Stochastic Volterra Integral Equations--- Representation of Adapted Solutions

Tianxiao Wang·Jiongmin Yong

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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.

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BibTeX RIS

Tianxiao Wang, Jiongmin Yong. 2018-02-10. Backward Stochastic Volterra Integral Equations--- Representation of Adapted Solutions. https://arxiv.org/abs/1802.03659

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