{"paper":{"title":"On the drawdown of completely asymmetric Levy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.RM"],"primary_cat":"math.PR","authors_text":"Aleksandar Mijatovic, Martijn R. Pistorius","submitted_at":"2011-03-08T08:23:14Z","abstract_excerpt":"The {\\em drawdown} process $Y$ of a completely asymmetric L\\'{e}vy process $X$ is equal to $X$ reflected at its running supremum $\\bar{X}$: $Y = \\bar{X} - X$. In this paper we explicitly express in terms of the scale function and the L\\'{e}vy measure of $X$ the law of the sextuple of the first-passage time of $Y$ over the level $a>0$, the time $\\bar{G}_{\\tau_a}$ of the last supremum of $X$ prior to $\\tau_a$, the infimum $\\unl X_{\\tau_a}$ and supremum $\\ovl X_{\\tau_a}$ of $X$ at $\\tau_a$ and the undershoot $a - Y_{\\tau_a-}$ and overshoot $Y_{\\tau_a}-a$ of $Y$ at $\\tau_a$. As application we obta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1460","kind":"arxiv","version":2},"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"}