{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:U55GXRXFFTRVQF3NDKFXHUNMVW","short_pith_number":"pith:U55GXRXF","schema_version":"1.0","canonical_sha256":"a77a6bc6e52ce358176d1a8b73d1acadb056b908e2c2c8375ec6bccc47919a64","source":{"kind":"arxiv","id":"1309.2469","version":3},"attestation_state":"computed","paper":{"title":"Riesz representation and optimal stopping with two case studies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Paavo Salminen, S\\\"oren Christensen","submitted_at":"2013-09-10T11:55:58Z","abstract_excerpt":"In this paper we demonstrate that the Riesz representation of excessive functions is a useful and enlightening tool to study optimal stopping problems. After a short general discussion of the Riesz representation we concretize, firstly, on a d-dimensional and, secondly, a space-time one-dimensional geometric Brownian motion. After this, two classical optimal stopping problems are discussed: 1) the optimal investment problem and 2) the valuation of the American put option. It is seen in both of these problems that the boundary of the stopping region can be characterized as a unique solution of "},"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":"1309.2469","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-10T11:55:58Z","cross_cats_sorted":[],"title_canon_sha256":"911b8448229945525c9dd81da38bc9e5e9325f114c6168df0b511e1cc9a23257","abstract_canon_sha256":"7a618f6b1ce3de02938798a652305f038d33a4bfa696648856428dc903fc357a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:47.199579Z","signature_b64":"H20f1oLrJE1T9nuaT201GfGOACH2FnNl3cfL/sWfpf97PEfF3fdS8WVKDh+KADnLXKDMxpdphXs61Nt3cYOyBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a77a6bc6e52ce358176d1a8b73d1acadb056b908e2c2c8375ec6bccc47919a64","last_reissued_at":"2026-05-18T01:29:47.198931Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:47.198931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Riesz representation and optimal stopping with two case studies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Paavo Salminen, S\\\"oren Christensen","submitted_at":"2013-09-10T11:55:58Z","abstract_excerpt":"In this paper we demonstrate that the Riesz representation of excessive functions is a useful and enlightening tool to study optimal stopping problems. After a short general discussion of the Riesz representation we concretize, firstly, on a d-dimensional and, secondly, a space-time one-dimensional geometric Brownian motion. After this, two classical optimal stopping problems are discussed: 1) the optimal investment problem and 2) the valuation of the American put option. It is seen in both of these problems that the boundary of the stopping region can be characterized as a unique solution of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2469","kind":"arxiv","version":3},"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":"1309.2469","created_at":"2026-05-18T01:29:47.199027+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.2469v3","created_at":"2026-05-18T01:29:47.199027+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2469","created_at":"2026-05-18T01:29:47.199027+00:00"},{"alias_kind":"pith_short_12","alias_value":"U55GXRXFFTRV","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"U55GXRXFFTRVQF3N","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"U55GXRXF","created_at":"2026-05-18T12:28:02.375192+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/U55GXRXFFTRVQF3NDKFXHUNMVW","json":"https://pith.science/pith/U55GXRXFFTRVQF3NDKFXHUNMVW.json","graph_json":"https://pith.science/api/pith-number/U55GXRXFFTRVQF3NDKFXHUNMVW/graph.json","events_json":"https://pith.science/api/pith-number/U55GXRXFFTRVQF3NDKFXHUNMVW/events.json","paper":"https://pith.science/paper/U55GXRXF"},"agent_actions":{"view_html":"https://pith.science/pith/U55GXRXFFTRVQF3NDKFXHUNMVW","download_json":"https://pith.science/pith/U55GXRXFFTRVQF3NDKFXHUNMVW.json","view_paper":"https://pith.science/paper/U55GXRXF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.2469&json=true","fetch_graph":"https://pith.science/api/pith-number/U55GXRXFFTRVQF3NDKFXHUNMVW/graph.json","fetch_events":"https://pith.science/api/pith-number/U55GXRXFFTRVQF3NDKFXHUNMVW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U55GXRXFFTRVQF3NDKFXHUNMVW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U55GXRXFFTRVQF3NDKFXHUNMVW/action/storage_attestation","attest_author":"https://pith.science/pith/U55GXRXFFTRVQF3NDKFXHUNMVW/action/author_attestation","sign_citation":"https://pith.science/pith/U55GXRXFFTRVQF3NDKFXHUNMVW/action/citation_signature","submit_replication":"https://pith.science/pith/U55GXRXFFTRVQF3NDKFXHUNMVW/action/replication_record"}},"created_at":"2026-05-18T01:29:47.199027+00:00","updated_at":"2026-05-18T01:29:47.199027+00:00"}