{"paper":{"title":"On the Ruin Probability of the Generalised Ornstein-Uhlenbeck Process in the Cram\\'er Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Claudia Kl\\\"uppelberg, Damien Bankowski, Ross Maller","submitted_at":"2011-01-05T17:20:52Z","abstract_excerpt":"For a bivariate \\Levy process $(\\xi_t,\\eta_t)_{t\\ge 0}$ and initial value $V_0$ define the Generalised Ornstein-Uhlenbeck (GOU) process \\[ V_t:=e^{\\xi_t}\\Big(V_0+\\int_0^t e^{-\\xi_{s-}}\\ud \\eta_s\\Big),\\quad t\\ge0,\\] and the associated stochastic integral process \\[Z_t:=\\int_0^t e^{-\\xi_{s-}}\\ud \\eta_s,\\quad t\\ge0.\\] Let $T_z:=\\inf\\{t>0:V_t<0\\mid V_0=z\\}$ and $\\psi(z):=P(T_z<\\infty)$ for $z\\ge 0$ be the ruin time and infinite horizon ruin probability of the GOU. Our results extend previous work of Nyrhinen (2001) and others to give asymptotic estimates for $\\psi(z)$ and the distribution of $T_z$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1034","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"}