{"paper":{"title":"Parisian Ruin of the Brownian Motion Risk Model with Constant Force of Interest","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Li Luo, Long Bai","submitted_at":"2016-06-23T15:08:07Z","abstract_excerpt":"Let $B(t), t\\in \\mathbb{R}$ be a standard Brownian motion. Define a risk process \\label{Rudef} R_u^{\\delta}(t)=e^{\\delta t}\\left(u+c\\int^{t}_{0}e^{-\\delta s}d s-\\sigma\\int_{0}^{t}e^{-\\delta s}d B(s)\\right), t\\geq0, where $u\\geq 0$ is the initial reserve, $\\delta\\geq0$ is the force of interest, $c>0$ is the rate of premium and $\\sigma>0$ is a volatility factor. In this contribution we obtain an approximation of the Parisian ruin probability \\mathcal{K}_S^{\\delta}(u,T_u):=\\mathbb{P}\\left\\{\\inf_{t\\in[0,S]} \\sup_{s\\in[t,t+T_u]} R_u^{\\delta}(s)<0\\right\\}, S\\ge 0, as $u\\rightarrow\\infty$ where $T_u$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07339","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"}