{"paper":{"title":"Two Applications of Brouwer's Fixed Point Theorem: in Insurance and in Biology Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OC","authors_text":"Muhamed Borogovac","submitted_at":"2015-03-09T02:13:09Z","abstract_excerpt":"In the first part of the article, a new interesting system of difference equations is introduced. It is developed for re-rating purposes in general insurance. A nonlinear transformation $\\varphi $ of a d-dimensional $(d \\ge 2)$ Euclidean space is introduced that enables us to express the system in the form $f^{t+1}:=\\varphi (f^t),\\, t=0,\\, 1,\\, 2,\\, \\ldots $. Under typical actuarial assumptions, existence of solutions of that system is proven by means of Brouwer's fixed point theorem in normed spaces. In addition, conditions that guarantee uniqueness of a solution are given. The second, smalle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04704","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"}