{"paper":{"title":"Finite-time ruin probability of aggregate Gaussian processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Enkelejd Hashorva, Krzysztof Debicki, Lanpeng Ji, Zhongquan Tan","submitted_at":"2014-04-23T07:57:51Z","abstract_excerpt":"Let $\\left\\{\\sum_{i=1}^n \\lambda_i X_i(t), t\\in [0,T]\\right\\}$ be an aggregate Gaussian risk process with $X_i, i\\leq n$ independent Gaussian processes satisfying Piterbarg conditions and $\\lambda_i$'s given positive weights. In this paper we derive exact asymptotics of the finite-time ruin probability given by $$\\mathbb{P}\\left(\\sup_{t\\in[0,T]}\\left(\\sum_{i=1}^n \\lambda_i X_i(t)- g(t) \\right)>u\\right)$$ as $u\\to\\infty$ for some general trend function $g$. Further, we derive asymptotic results for the finite-time ruin probabilities of risk processes perturbed by an aggregate Gaussian process."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5730","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"}