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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 $T_u$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1606.07339","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-06-23T15:08:07Z","cross_cats_sorted":[],"title_canon_sha256":"2afc63bfb6ab2a3c1e43a56759008f3f707225e0642fa85667a80be19fa6b7d8","abstract_canon_sha256":"153a2fee2c6b1079ae69c5411efe3e0c4c3e3fdfdc30454789c31b441b9ad40b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:43.247410Z","signature_b64":"g/iRAfB0Ss5DIyi/CNqJhdxBCZ/1IeQ9dlrWazhzwv634kntwTO1TXDf1I+uwPWIBSVp9XI7b2zFw1BiuSuTDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3848c378ef9176cb43fbe0d43d8831eaccf8329918a2ec3231ee93e5367224f4","last_reissued_at":"2026-05-18T01:04:43.246928Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:43.246928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1606.07339","created_at":"2026-05-18T01:04:43.247001+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.07339v2","created_at":"2026-05-18T01:04:43.247001+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07339","created_at":"2026-05-18T01:04:43.247001+00:00"},{"alias_kind":"pith_short_12","alias_value":"HBEMG6HPSF3M","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"HBEMG6HPSF3MWQ73","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"HBEMG6HP","created_at":"2026-05-18T12:30:19.053100+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HBEMG6HPSF3MWQ734DKD3CBR5L","json":"https://pith.science/pith/HBEMG6HPSF3MWQ734DKD3CBR5L.json","graph_json":"https://pith.science/api/pith-number/HBEMG6HPSF3MWQ734DKD3CBR5L/graph.json","events_json":"https://pith.science/api/pith-number/HBEMG6HPSF3MWQ734DKD3CBR5L/events.json","paper":"https://pith.science/paper/HBEMG6HP"},"agent_actions":{"view_html":"https://pith.science/pith/HBEMG6HPSF3MWQ734DKD3CBR5L","download_json":"https://pith.science/pith/HBEMG6HPSF3MWQ734DKD3CBR5L.json","view_paper":"https://pith.science/paper/HBEMG6HP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.07339&json=true","fetch_graph":"https://pith.science/api/pith-number/HBEMG6HPSF3MWQ734DKD3CBR5L/graph.json","fetch_events":"https://pith.science/api/pith-number/HBEMG6HPSF3MWQ734DKD3CBR5L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HBEMG6HPSF3MWQ734DKD3CBR5L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HBEMG6HPSF3MWQ734DKD3CBR5L/action/storage_attestation","attest_author":"https://pith.science/pith/HBEMG6HPSF3MWQ734DKD3CBR5L/action/author_attestation","sign_citation":"https://pith.science/pith/HBEMG6HPSF3MWQ734DKD3CBR5L/action/citation_signature","submit_replication":"https://pith.science/pith/HBEMG6HPSF3MWQ734DKD3CBR5L/action/replication_record"}},"created_at":"2026-05-18T01:04:43.247001+00:00","updated_at":"2026-05-18T01:04:43.247001+00:00"}