{"paper":{"title":"Strategic Risk Reduction: Self-Protection and Self-Insurance","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"q-fin.RM","authors_text":"Wing Fung Chong","submitted_at":"2026-06-29T14:27:40Z","abstract_excerpt":"This paper studies how a risk holder should combine self-protection and self-insurance when market insurance is absent. In a Bernoulli loss model, self-protection reduces the residual loss probability, while self-insurance reduces the residual loss severity. The risk holder evaluates residual risk using either Value-at-Risk or Tail Value-at-Risk and incurs a joint risk-reduction cost that allows technological interaction between the two activities. We show that Value-at-Risk leads to a threshold-driven solution that the optimal strategy is either no risk reduction, pure self-protection, or pur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30363","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.30363/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}