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arXiv · 2609.06045

C\`adl\`ag Solutions to Backward Stochastic Dynamics featuring Oblique Subgradients and driven by Martingale Noise

Andreea Negruţ·Aurel Răşcanu·Eduard Rotenstein
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Abstract

The present study improves the qualitative analysis of backward stochastic variational dynamics on a general complete filtered probability space, considered in the spirit of Liang, Lyons and Qian (2011). Our primary objective is to overcome a substantial limitation in the study of Bensoussan, Li and Yam (2018), where the boundedness condition imposed on the multivalued subdifferential operator excludes standard obstacle-type constraints and indicator functions of convex sets. We prove the existence and uniqueness of a strong c\`adl\`ag solution under the natural assumption that the driving proper lower semicontinuous convex function is merely bounded from below by an affine/quadratic function. Furthermore, we incorporate an oblique reflection governed by a time-dependent, uniformly positive definite symmetric matrix, in the spirit of the pioneering results of Gassous, R\u{a}\c{s}canu and Rotenstein (2012, 2015).

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Andreea Negruţ, Aurel Răşcanu, Eduard Rotenstein. 2026-09-05. C\`adl\`ag Solutions to Backward Stochastic Dynamics featuring Oblique Subgradients and driven by Martingale Noise. https://arxiv.org/abs/2609.06045

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