{"paper":{"title":"Path decomposition of ruinous behavior for a general L\\'{e}vy insurance risk process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Philip S. Griffin, Ross A. Maller","submitted_at":"2011-06-29T12:01:01Z","abstract_excerpt":"We analyze the general L\\'{e}vy insurance risk process for L\\'{e}vy measures in the convolution equivalence class $\\mathcal{S}^{(\\alpha)}$, $\\alpha>0$, via a new kind of path decomposition. This yields a very general functional limit theorem as the initial reserve level $u\\to \\infty$, and a host of new results for functionals of interest in insurance risk. Particular emphasis is placed on the time to ruin, which is shown to have a proper limiting distribution, as $u\\to \\infty$, conditional on ruin occurring under our assumptions. Existing asymptotic results under the $\\mathcal{S}^{(\\alpha)}$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5915","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"}