{"paper":{"title":"Ruin probability in the presence of risky investments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","q-fin.CP"],"primary_cat":"q-fin.RM","authors_text":"Serguei Pergamenchtchikov (LMRS), Zeitouny Omar (LMRS)","submitted_at":"2010-11-05T06:19:33Z","abstract_excerpt":"We consider an insurance company in the case when the premium rate is a bounded non-negative random function $c_\\zs{t}$ and the capital of the insurance company is invested in a risky asset whose price follows a geometric Brownian motion with mean return $a$ and volatility $\\sigma>0$. If $\\beta:=2a/\\sigma^2-1>0$ we find exact the asymptotic upper and lower bounds for the ruin probability $\\Psi(u)$ as the initial endowment $u$ tends to infinity, i.e. we show that $C_*u^{-\\beta}\\le\\Psi(u)\\le C^*u^{-\\beta}$ for sufficiently large $u$. Moreover if $c_\\zs{t}=c^*e^{\\gamma t}$ with $\\gamma\\le 0$ we f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1329","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"}