{"paper":{"title":"A Note on Applications of Stochastic Ordering to Control Problems in Insurance and Finance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.PM"],"primary_cat":"math.PR","authors_text":"Erhan Bayraktar, Nicole Bauerle","submitted_at":"2012-10-14T14:44:35Z","abstract_excerpt":"We consider a controlled diffusion process $(X_t)_{t\\ge 0}$ where the controller is allowed to choose the drift $\\mu_t$ and the volatility $\\sigma_t$ from a set $\\K(x) \\subset \\R\\times (0,\\infty)$ when $X_t=x$. By choosing the largest $\\frac{\\mu}{\\sigma^2}$ at every point in time an extremal process is constructed which is under suitable time changes stochastically larger than any other admissible process. This observation immediately leads to a very simple solution of problems where ruin or hitting probabilities have to be minimized. Under further conditions this extremal process also minimiz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3800","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"}