{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:4QRFLP3YIYCUQKPA5ID43U2UPY","short_pith_number":"pith:4QRFLP3Y","schema_version":"1.0","canonical_sha256":"e42255bf7846054829e0ea07cdd3547e1adee3cdcf3f1d3adbb8f5bac8aec955","source":{"kind":"arxiv","id":"1201.2257","version":4},"attestation_state":"computed","paper":{"title":"Risk Measures on $\\mathcal{P}(\\mathbb{R})$ and Value At Risk with Probability/Loss function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-fin.RM","authors_text":"Ilaria Peri, Marco Frittelli, Marco Maggis","submitted_at":"2012-01-11T08:19:43Z","abstract_excerpt":"We propose a generalization of the classical notion of the $V@R_{\\lambda}$ that takes into account not only the probability of the losses, but the balance between such probability and the amount of the loss. This is obtained by defining a new class of law invariant risk measures based on an appropriate family of acceptance sets. The $V@R_{\\lambda}$ and other known law invariant risk measures turn out to be special cases of our proposal. We further prove the dual representation of Risk Measures on $\\mathcal{P}(% \\mathbb{R}).$"},"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":"1201.2257","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2012-01-11T08:19:43Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"5661937d23ed0fa1cec165259557bd304a814d0c3aaa4e9549a2dc78f9dfc4f9","abstract_canon_sha256":"853ae72fe6b46264c7c2ec4674b9ea94660d34518a51a1d1a9ab2e9a1ec6b596"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:15.199541Z","signature_b64":"vN6hzKqyx4mr/RL8GPJSg8YmZ0VA/VjbrBXSsxGse6FdqcboFXrQn1/utU9F+r+0DMEeYeHRQ6bz0oTngWagCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e42255bf7846054829e0ea07cdd3547e1adee3cdcf3f1d3adbb8f5bac8aec955","last_reissued_at":"2026-05-18T03:46:15.198710Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:15.198710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Risk Measures on $\\mathcal{P}(\\mathbb{R})$ and Value At Risk with Probability/Loss function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-fin.RM","authors_text":"Ilaria Peri, Marco Frittelli, Marco Maggis","submitted_at":"2012-01-11T08:19:43Z","abstract_excerpt":"We propose a generalization of the classical notion of the $V@R_{\\lambda}$ that takes into account not only the probability of the losses, but the balance between such probability and the amount of the loss. This is obtained by defining a new class of law invariant risk measures based on an appropriate family of acceptance sets. The $V@R_{\\lambda}$ and other known law invariant risk measures turn out to be special cases of our proposal. We further prove the dual representation of Risk Measures on $\\mathcal{P}(% \\mathbb{R}).$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2257","kind":"arxiv","version":4},"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":"1201.2257","created_at":"2026-05-18T03:46:15.198826+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.2257v4","created_at":"2026-05-18T03:46:15.198826+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.2257","created_at":"2026-05-18T03:46:15.198826+00:00"},{"alias_kind":"pith_short_12","alias_value":"4QRFLP3YIYCU","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"4QRFLP3YIYCUQKPA","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"4QRFLP3Y","created_at":"2026-05-18T12:26:53.410803+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/4QRFLP3YIYCUQKPA5ID43U2UPY","json":"https://pith.science/pith/4QRFLP3YIYCUQKPA5ID43U2UPY.json","graph_json":"https://pith.science/api/pith-number/4QRFLP3YIYCUQKPA5ID43U2UPY/graph.json","events_json":"https://pith.science/api/pith-number/4QRFLP3YIYCUQKPA5ID43U2UPY/events.json","paper":"https://pith.science/paper/4QRFLP3Y"},"agent_actions":{"view_html":"https://pith.science/pith/4QRFLP3YIYCUQKPA5ID43U2UPY","download_json":"https://pith.science/pith/4QRFLP3YIYCUQKPA5ID43U2UPY.json","view_paper":"https://pith.science/paper/4QRFLP3Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.2257&json=true","fetch_graph":"https://pith.science/api/pith-number/4QRFLP3YIYCUQKPA5ID43U2UPY/graph.json","fetch_events":"https://pith.science/api/pith-number/4QRFLP3YIYCUQKPA5ID43U2UPY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4QRFLP3YIYCUQKPA5ID43U2UPY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4QRFLP3YIYCUQKPA5ID43U2UPY/action/storage_attestation","attest_author":"https://pith.science/pith/4QRFLP3YIYCUQKPA5ID43U2UPY/action/author_attestation","sign_citation":"https://pith.science/pith/4QRFLP3YIYCUQKPA5ID43U2UPY/action/citation_signature","submit_replication":"https://pith.science/pith/4QRFLP3YIYCUQKPA5ID43U2UPY/action/replication_record"}},"created_at":"2026-05-18T03:46:15.198826+00:00","updated_at":"2026-05-18T03:46:15.198826+00:00"}