{"paper":{"title":"Locally Lipschitz BSDE driven by a continuous martingale: path-derivative approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kihun Nam","submitted_at":"2016-06-13T07:05:33Z","abstract_excerpt":"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 $M$ from $0$ to $t$ and $m$ is defined by $[M,M]_{t}=\\int_{0}^{t}m_{s}m_{s}^{*}d{\\rm tr}[M,M]_{s}$. When the BSDE is one-dimensional, we could show the existence and uniqueness of solution. On the contrary, when the BSDE is multidimensional,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03836","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}