{"paper":{"title":"Approximation of passage times of gamma-reflected processes with fBm input","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Enkelejd Hashorva, Lanpeng Ji","submitted_at":"2013-10-11T13:12:57Z","abstract_excerpt":"Define a gamma-reflected process W_\\gamma(t)=Y_H(t)-\\gamma\\inf_{s\\in[0,t]}Y_H(s), t\\ge0 with input process {Y_H(t), t\\ge 0} which is a fractional Brownian motion with Hurst index H\\in (0,1) and a negative linear trend. In risk theory {u-W_\\gamma(t), t\\ge 0} is referred to as the risk process with tax payments of a loss-carry-forward type. For various risk processes numerous results are known for the approximation of the first and last passage times to 0 (ruin times) when the initial reserve $u$ goes to infinity. In this paper we show that for the gamma-reflected process the conditional (standa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3114","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"}