{"paper":{"title":"Optimal control of predictive mean-field equations and applications to finance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.PM"],"primary_cat":"math.OC","authors_text":"Agn\\`Es Sulem, Bernt {\\O}ksendal","submitted_at":"2015-05-19T09:24:45Z","abstract_excerpt":"We study a coupled system of controlled stochastic differential equations (SDEs) driven by a Brownian motion and a compensated Poisson random measure, consisting of a forward SDE in the unknown process $X(t)$ and a \\emph{predictive mean-field} backward SDE (BSDE) in the unknowns $Y(t), Z(t), K(t,\\cdot)$. The driver of the BSDE at time $t$ may depend not just upon the unknown processes $Y(t), Z(t), K(t,\\cdot)$, but also on the predicted future value $Y(t+\\delta)$, defined by the conditional expectation $A(t):= E[Y(t+\\delta) | \\mathcal{F}_t]$. \\\\ We give a sufficient and a necessary maximum prin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04921","kind":"arxiv","version":1},"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"}