{"paper":{"title":"Fluctuation theory for level-dependent L\\'evy risk processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Irmina Czarna, Jos\\'e-Luis P\\'erez, Kazutoshi Yamazaki, Tomasz Rolski","submitted_at":"2017-11-30T19:48:41Z","abstract_excerpt":"A level-dependent L\\'evy process solves the stochastic differential equation $dU(t) = dX(t)-{\\phi}(U(t)) dt$, where $X$ is a spectrally negative L\\'evy process. A special case is a multi-refracted L\\'evy process with $\\phi_k(x)=\\sum_{j=1}^k\\delta_j1_{\\{x\\geq b_j\\}}$. A general rate function $\\phi$ that is non-decreasing and continuously differentiable is also considered. We discuss solutions of the above stochastic differential equation and investigate the so-called scale functions, which are counterparts of the scale functions from the theory of L\\'evy processes. We show how fluctuation ident"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00050","kind":"arxiv","version":2},"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"}