{"paper":{"title":"Ruin problem for Brownian motion risk model with interest rate and tax payment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Long Bai, Peng Liu","submitted_at":"2018-06-13T08:29:07Z","abstract_excerpt":"Let $\\{B(t), t\\ge 0\\}$ be a Brownian motion. Consider the Brownian motion risk model with interest rate collection and tax payment defined by \\begin{align}\\label{Rudef} \\widetilde{U}_\\gamma^\\delta(t)=\\widetilde{X}^\\delta(t)-\\gamma\\sup_{s\\in[0,t]} \\left(\\widetilde{X}^\\delta(s)e^{\\delta(t-s)}-ue^{\\delta(t-s)}\\right),t\\ge0, \\end{align} with $$\\widetilde{X}^\\delta(t)=ue^{\\delta t}+c \\int_0^t e^{\\delta (t-v)}dv-\\sigma \\int_0^t e^{\\delta(t-v)}dB(v),$$ where $c>0,\\gamma \\in [0,1)$ and $\\delta \\in \\mathbb{R}$ are three given constants. When $\\delta=0$ and $\\gamma \\in (0,1)$ this is the risk model intr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04889","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"}