{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:OIECSQ7XRZ4RATKKPBFY6OXBDL","short_pith_number":"pith:OIECSQ7X","canonical_record":{"source":{"id":"1308.5152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2013-08-23T15:10:44Z","cross_cats_sorted":["math.OC","math.PR"],"title_canon_sha256":"831916b4c232718c5750f988bd72eddd6685f7027487113d1b799977c5e18a08","abstract_canon_sha256":"157f16004e68b57ce3ee410c8bd7633c2d104aedad53808576bb3262ddfbf6f0"},"schema_version":"1.0"},"canonical_sha256":"72082943f78e79104d4a784b8f3ae11afe2d91e2fddfb004b18549cf1fc80153","source":{"kind":"arxiv","id":"1308.5152","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5152","created_at":"2026-05-18T03:15:08Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5152v1","created_at":"2026-05-18T03:15:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5152","created_at":"2026-05-18T03:15:08Z"},{"alias_kind":"pith_short_12","alias_value":"OIECSQ7XRZ4R","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OIECSQ7XRZ4RATKK","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OIECSQ7X","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:OIECSQ7XRZ4RATKKPBFY6OXBDL","target":"record","payload":{"canonical_record":{"source":{"id":"1308.5152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2013-08-23T15:10:44Z","cross_cats_sorted":["math.OC","math.PR"],"title_canon_sha256":"831916b4c232718c5750f988bd72eddd6685f7027487113d1b799977c5e18a08","abstract_canon_sha256":"157f16004e68b57ce3ee410c8bd7633c2d104aedad53808576bb3262ddfbf6f0"},"schema_version":"1.0"},"canonical_sha256":"72082943f78e79104d4a784b8f3ae11afe2d91e2fddfb004b18549cf1fc80153","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:08.004056Z","signature_b64":"WlkSVqKLgZZYZLUbNeYqhYjt2+t3ckOqXwkyu/pc7FUcEaSiYV2lVOOK5RbGTfv2DZ2RLeba81sjLbqpTn/SBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72082943f78e79104d4a784b8f3ae11afe2d91e2fddfb004b18549cf1fc80153","last_reissued_at":"2026-05-18T03:15:08.003344Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:08.003344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.5152","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:15:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gR0JTE0dt1IpmCMwAuonlTckDuSzJ5IlIRFoTGi1uo0QL1mKZ3956cKLiggu7xIhlRD7Yy7R4UVafa365pruDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:20:21.499698Z"},"content_sha256":"b91ddcb01cbc4c350d1571f1361262fba48072fd5fb912db1d1106a371774be8","schema_version":"1.0","event_id":"sha256:b91ddcb01cbc4c350d1571f1361262fba48072fd5fb912db1d1106a371774be8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:OIECSQ7XRZ4RATKKPBFY6OXBDL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computation of ruin probabilities for general discrete-time Markov models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","math.PR"],"primary_cat":"q-fin.RM","authors_text":"Alessandro Abate, Ilya Tkachev","submitted_at":"2013-08-23T15:10:44Z","abstract_excerpt":"We study the ruin problem over a risk process described by a discrete-time Markov model. In contrast to previous studies that focused on the asymptotic behaviour of ruin probabilities for large values of the initial capital, we provide a new technique to compute the quantity of interest for any initial value, and with any given precision. Rather than focusing on a particular model for risk processes, we give a general characterization of the ruin probability by providing corresponding recursions and fixpoint equations. Since such equations for the ruin probability are ill-posed in the sense th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5152","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:15:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nhkop6X9uyPj6YEnr78354EUxCKgLq63+U1TxqZle84yYNDy4BXNYAUl7+DQRcaiz+6nXy83fHh81hR+kC9gAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:20:21.500239Z"},"content_sha256":"311cfbde5bec9ff5add7ddeabc7c75c2dbdad16018615061f673e4742711420a","schema_version":"1.0","event_id":"sha256:311cfbde5bec9ff5add7ddeabc7c75c2dbdad16018615061f673e4742711420a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OIECSQ7XRZ4RATKKPBFY6OXBDL/bundle.json","state_url":"https://pith.science/pith/OIECSQ7XRZ4RATKKPBFY6OXBDL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OIECSQ7XRZ4RATKKPBFY6OXBDL/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":"2026-06-04T17:20:21Z","links":{"resolver":"https://pith.science/pith/OIECSQ7XRZ4RATKKPBFY6OXBDL","bundle":"https://pith.science/pith/OIECSQ7XRZ4RATKKPBFY6OXBDL/bundle.json","state":"https://pith.science/pith/OIECSQ7XRZ4RATKKPBFY6OXBDL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OIECSQ7XRZ4RATKKPBFY6OXBDL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OIECSQ7XRZ4RATKKPBFY6OXBDL","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":"157f16004e68b57ce3ee410c8bd7633c2d104aedad53808576bb3262ddfbf6f0","cross_cats_sorted":["math.OC","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2013-08-23T15:10:44Z","title_canon_sha256":"831916b4c232718c5750f988bd72eddd6685f7027487113d1b799977c5e18a08"},"schema_version":"1.0","source":{"id":"1308.5152","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5152","created_at":"2026-05-18T03:15:08Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5152v1","created_at":"2026-05-18T03:15:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5152","created_at":"2026-05-18T03:15:08Z"},{"alias_kind":"pith_short_12","alias_value":"OIECSQ7XRZ4R","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OIECSQ7XRZ4RATKK","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OIECSQ7X","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:311cfbde5bec9ff5add7ddeabc7c75c2dbdad16018615061f673e4742711420a","target":"graph","created_at":"2026-05-18T03:15:08Z","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 study the ruin problem over a risk process described by a discrete-time Markov model. In contrast to previous studies that focused on the asymptotic behaviour of ruin probabilities for large values of the initial capital, we provide a new technique to compute the quantity of interest for any initial value, and with any given precision. Rather than focusing on a particular model for risk processes, we give a general characterization of the ruin probability by providing corresponding recursions and fixpoint equations. Since such equations for the ruin probability are ill-posed in the sense th","authors_text":"Alessandro Abate, Ilya Tkachev","cross_cats":["math.OC","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2013-08-23T15:10:44Z","title":"Computation of ruin probabilities for general discrete-time Markov models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5152","kind":"arxiv","version":1},"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:b91ddcb01cbc4c350d1571f1361262fba48072fd5fb912db1d1106a371774be8","target":"record","created_at":"2026-05-18T03:15:08Z","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":"157f16004e68b57ce3ee410c8bd7633c2d104aedad53808576bb3262ddfbf6f0","cross_cats_sorted":["math.OC","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2013-08-23T15:10:44Z","title_canon_sha256":"831916b4c232718c5750f988bd72eddd6685f7027487113d1b799977c5e18a08"},"schema_version":"1.0","source":{"id":"1308.5152","kind":"arxiv","version":1}},"canonical_sha256":"72082943f78e79104d4a784b8f3ae11afe2d91e2fddfb004b18549cf1fc80153","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72082943f78e79104d4a784b8f3ae11afe2d91e2fddfb004b18549cf1fc80153","first_computed_at":"2026-05-18T03:15:08.003344Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:08.003344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WlkSVqKLgZZYZLUbNeYqhYjt2+t3ckOqXwkyu/pc7FUcEaSiYV2lVOOK5RbGTfv2DZ2RLeba81sjLbqpTn/SBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:08.004056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.5152","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b91ddcb01cbc4c350d1571f1361262fba48072fd5fb912db1d1106a371774be8","sha256:311cfbde5bec9ff5add7ddeabc7c75c2dbdad16018615061f673e4742711420a"],"state_sha256":"284939c7ddde4fd6fd3fbd2d7a9f89845b32b7190c71fbf8f91b7214930ccd9f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1m8RuFB0RBK1hg9+q3tQ5rAILtdQwZaoEVgs0PIOufcIKij6jT8ZG4vtvRqXbVwg6Sd1cZlxkrSxmEGQoeS1AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T17:20:21.503114Z","bundle_sha256":"e6ecb8af3711bb93927e33eda51a99c5b20cd422fb55cd47cb68454d445176bd"}}