Càdlàg Solutions to Backward Stochastic Dynamics featuring Oblique Subgradients and driven by Martingale Noise
Andreea Negruţ, Aurel Răşcanu, Eduard Rotenstein
Source 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 càdlàg 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, Răşcanu and Rotenstein (2012, 2015).
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