{"paper":{"title":"On generalized CIR equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jerzy Zabczyk, Michal Barski","submitted_at":"2019-02-24T16:49:30Z","abstract_excerpt":"The paper is concerned with stochastic equations for the short rate process $R$ $$ dR(t)=F(R(t))dt+G(R(t-))dZ(t), $$ in the affine model of the bond prices. The equation is driven by a L\\'evy martingale $Z$. It is shown that the discounted bond prices are local martingales if either $Z$ is a stable process of index $\\alpha\\in(1,2]$,\\,$F(x)= ax +b, b\\geq 0$, $G(x)=cx^{1/\\alpha}, c>0$ or $Z$ must be a L\\'evy martingale with positive jumps and trajectories of bounded variation, $F(x)= ax +b, b\\geq 0$ and G is a constant. The result generalizes the well known Cox-Ingersoll-Ross result and extends "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08976","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"}