{"paper":{"title":"A Weak Dynamic Programming Principle for Combined Optimal Stopping and Stochastic Control with $\\mathcal{E}^f$- expectations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Agn\\`Es Sulem, Marie-Claire Quenez, Roxana Dumitrescu","submitted_at":"2014-07-01T21:59:30Z","abstract_excerpt":"We study a combined optimal control/stopping problem under a nonlinear expectation ${\\cal E}^f$ induced by a BSDE with jumps, in a Markovian framework. The terminal reward function is only supposed to be Borelian. The value function $u$ associated with this problem is generally irregular. We first establish a {\\em sub- (resp. super-) optimality principle of dynamic programming} involving its {\\em upper- (resp. lower-) semicontinuous envelope} $u^*$ (resp. $u_*$). This result, called {\\em weak} dynamic programming principle (DPP), extends that obtained in \\cite{BT} in the case of a classical ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0416","kind":"arxiv","version":5},"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"}