{"paper":{"title":"A filtering approach to tracking volatility from prices observed at random times","license":"","headline":"","cross_cats":["q-fin.ST"],"primary_cat":"math.PR","authors_text":"Boris Rozovskii, Jak\\v{s}a Cvitani\\'c, Robert Liptser","submitted_at":"2006-12-08T11:09:49Z","abstract_excerpt":"This paper is concerned with nonlinear filtering of the coefficients in asset price models with stochastic volatility. More specifically, we assume that the asset price process $S=(S_{t})_{t\\geq0}$ is given by \\[ dS_{t}=m(\\theta_{t})S_{t} dt+v(\\theta_{t})S_{t} dB_{t}, \\] where $B=(B_{t})_{t\\geq0}$ is a Brownian motion, $v$ is a positive function and $\\theta=(\\theta_{t})_{t\\geq0}$ is a c\\'{a}dl\\'{a}g strong Markov process. The random process $\\theta$ is unobservable. We assume also that the asset price $S_{t}$ is observed only at random times $0<\\tau_{1}<\\tau_{2}<....$ This is an appropriate as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612212","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"}