Locally Lipschitz BSDE driven by a continuous martingale a path-derivative approach
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DOI: 10.1016/j.spa.2021.09.009
Abstract: Using a new notion of path-derivative, we study well-posedness of backward stochastic differential equation driven by a continuous martingale $M$ when $f(s,\gamma,y,z)$ is locally Lipschitz in $(y,z)$: \[Y_{t}=\xi(M_{[0,T]})+\int_{t}^{T}f(s,M_{[0,s]},Y_{s-},Z_{s}m_{s})d{\rm tr}[M,M]_{s}-\int_{t}^{T}Z_{s}dM_{s}-N_{T}+N_{t}\] Here, $M_{[0,t]}$ is the path of… read more here.
Keywords: lipschitz bsde; driven continuous; path; path derivative ... See more keywords