{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DV3W6L4RZNYLBUS2HWVRYK76U3","short_pith_number":"pith:DV3W6L4R","canonical_record":{"source":{"id":"1808.02182","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-07T01:55:51Z","cross_cats_sorted":[],"title_canon_sha256":"384c868326f3b00a163df4aa6b405a6cfe78bf4a9c9f3db94b317eea4ca25bf3","abstract_canon_sha256":"86991dfbcc6e5ccca45344cabfade2fc54d5a69349e83a2ff79de8b1066940b7"},"schema_version":"1.0"},"canonical_sha256":"1d776f2f91cb70b0d25a3dab1c2bfea6c00b635c48a55a2ad9d57e5fe4665036","source":{"kind":"arxiv","id":"1808.02182","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02182","created_at":"2026-05-18T00:05:29Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02182v2","created_at":"2026-05-18T00:05:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02182","created_at":"2026-05-18T00:05:29Z"},{"alias_kind":"pith_short_12","alias_value":"DV3W6L4RZNYL","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DV3W6L4RZNYLBUS2","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DV3W6L4R","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DV3W6L4RZNYLBUS2HWVRYK76U3","target":"record","payload":{"canonical_record":{"source":{"id":"1808.02182","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-07T01:55:51Z","cross_cats_sorted":[],"title_canon_sha256":"384c868326f3b00a163df4aa6b405a6cfe78bf4a9c9f3db94b317eea4ca25bf3","abstract_canon_sha256":"86991dfbcc6e5ccca45344cabfade2fc54d5a69349e83a2ff79de8b1066940b7"},"schema_version":"1.0"},"canonical_sha256":"1d776f2f91cb70b0d25a3dab1c2bfea6c00b635c48a55a2ad9d57e5fe4665036","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:29.984048Z","signature_b64":"ykjPcvWXhjJEDoyRJB4nvU1YRkFs4W27UhYa/fjNuKaFT/u/EZPO2GrDeQVYTVwJ2p9EHHqqJg0N2/MMMPOcAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d776f2f91cb70b0d25a3dab1c2bfea6c00b635c48a55a2ad9d57e5fe4665036","last_reissued_at":"2026-05-18T00:05:29.983418Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:29.983418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.02182","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:05:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"awwD6X6V4gtiYY3En3mhX4Hfh+Kos2vtqoDvN3lp74Txa/WmwpwTKcJPHu3XHsYuffvpQHJtuTOHzOAkZRboBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:24:27.493444Z"},"content_sha256":"e1fbfb00c5a3815167ff0d24fca3a1ebc051fd01544b148f5c4109fb4d7778c1","schema_version":"1.0","event_id":"sha256:e1fbfb00c5a3815167ff0d24fca3a1ebc051fd01544b148f5c4109fb4d7778c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DV3W6L4RZNYLBUS2HWVRYK76U3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal bail-out dividends problem with transaction cost and capital injection constraint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Harold Moreno-Franco, Jos\\'e Luis P\\'erez, Mauricio Junca","submitted_at":"2018-08-07T01:55:51Z","abstract_excerpt":"We consider the bail-out optimal dividend problem under fixed transaction costs for a L\\'evy risk model. Furthermore, we consider the version with a constraint expected net present value of injected capital. To characterize the solution to the aforementioned models, we first solve the bail-out optimal dividend problem under transaction costs and capital injection and show the optimality of reflected (c1; c2)- policies. Next, we introduce the dual Lagrangian problem and show that the complementary slackness conditions are satisfied, characterizing the optimal Lagrange multiplier. Finally, we il"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02182","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:05:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NnzfS0U1PRXrVfMraBGsNAybdDpRxCmU3YJOi6728gO/qwV4mxANscVpVbRvhBgN+zMIMEMEXXfqx7x9tY0wAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:24:27.494043Z"},"content_sha256":"4fe93a03d56be969a0a42504a6af0bfa1fb551e540b0c9963421f7589394c556","schema_version":"1.0","event_id":"sha256:4fe93a03d56be969a0a42504a6af0bfa1fb551e540b0c9963421f7589394c556"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DV3W6L4RZNYLBUS2HWVRYK76U3/bundle.json","state_url":"https://pith.science/pith/DV3W6L4RZNYLBUS2HWVRYK76U3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DV3W6L4RZNYLBUS2HWVRYK76U3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T09:24:27Z","links":{"resolver":"https://pith.science/pith/DV3W6L4RZNYLBUS2HWVRYK76U3","bundle":"https://pith.science/pith/DV3W6L4RZNYLBUS2HWVRYK76U3/bundle.json","state":"https://pith.science/pith/DV3W6L4RZNYLBUS2HWVRYK76U3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DV3W6L4RZNYLBUS2HWVRYK76U3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DV3W6L4RZNYLBUS2HWVRYK76U3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"86991dfbcc6e5ccca45344cabfade2fc54d5a69349e83a2ff79de8b1066940b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-07T01:55:51Z","title_canon_sha256":"384c868326f3b00a163df4aa6b405a6cfe78bf4a9c9f3db94b317eea4ca25bf3"},"schema_version":"1.0","source":{"id":"1808.02182","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02182","created_at":"2026-05-18T00:05:29Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02182v2","created_at":"2026-05-18T00:05:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02182","created_at":"2026-05-18T00:05:29Z"},{"alias_kind":"pith_short_12","alias_value":"DV3W6L4RZNYL","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DV3W6L4RZNYLBUS2","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DV3W6L4R","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:4fe93a03d56be969a0a42504a6af0bfa1fb551e540b0c9963421f7589394c556","target":"graph","created_at":"2026-05-18T00:05:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider the bail-out optimal dividend problem under fixed transaction costs for a L\\'evy risk model. Furthermore, we consider the version with a constraint expected net present value of injected capital. To characterize the solution to the aforementioned models, we first solve the bail-out optimal dividend problem under transaction costs and capital injection and show the optimality of reflected (c1; c2)- policies. Next, we introduce the dual Lagrangian problem and show that the complementary slackness conditions are satisfied, characterizing the optimal Lagrange multiplier. Finally, we il","authors_text":"Harold Moreno-Franco, Jos\\'e Luis P\\'erez, Mauricio Junca","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-07T01:55:51Z","title":"Optimal bail-out dividends problem with transaction cost and capital injection constraint"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02182","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e1fbfb00c5a3815167ff0d24fca3a1ebc051fd01544b148f5c4109fb4d7778c1","target":"record","created_at":"2026-05-18T00:05:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"86991dfbcc6e5ccca45344cabfade2fc54d5a69349e83a2ff79de8b1066940b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-07T01:55:51Z","title_canon_sha256":"384c868326f3b00a163df4aa6b405a6cfe78bf4a9c9f3db94b317eea4ca25bf3"},"schema_version":"1.0","source":{"id":"1808.02182","kind":"arxiv","version":2}},"canonical_sha256":"1d776f2f91cb70b0d25a3dab1c2bfea6c00b635c48a55a2ad9d57e5fe4665036","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d776f2f91cb70b0d25a3dab1c2bfea6c00b635c48a55a2ad9d57e5fe4665036","first_computed_at":"2026-05-18T00:05:29.983418Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:29.983418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ykjPcvWXhjJEDoyRJB4nvU1YRkFs4W27UhYa/fjNuKaFT/u/EZPO2GrDeQVYTVwJ2p9EHHqqJg0N2/MMMPOcAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:29.984048Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.02182","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1fbfb00c5a3815167ff0d24fca3a1ebc051fd01544b148f5c4109fb4d7778c1","sha256:4fe93a03d56be969a0a42504a6af0bfa1fb551e540b0c9963421f7589394c556"],"state_sha256":"54f79005d25dc0a241cdb3f7e12d518b22d3ea2537c081801e3ae2bb866c9663"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U1z1XVwf8b6hlXPhJAnTaNqMG0Dup4H/Fe1qthaWORWTOG9YBRIMwrE+zU5Usaj5eS2/GF84YjpgI2xLl+3ACw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T09:24:27.496876Z","bundle_sha256":"524e0b1922f672440a4bce54343fa50e1abd1c5c7988bdf55585c77e580b9a94"}}