{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:11:34Z","timestamp":1776784294278,"version":"3.51.2"},"reference-count":19,"publisher":"American Mathematical Society (AMS)","issue":"251","license":[{"start":{"date-parts":[[2005,10,5]],"date-time":"2005-10-05T00:00:00Z","timestamp":1128470400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>This paper completes a previous work on a Black and Scholes equation with stochastic volatility. This is a degenerate parabolic equation, which gives the price of a European option as a function of the time, of the price of the underlying asset, and of the volatility, when the volatility is a function of a mean reverting Orstein\u2013Uhlenbeck process, possibly correlated with the underlying asset. The analysis involves weighted Sobolev spaces. We give a characterization of the domain of the operator, which permits us to use results from the theory of semigroups. We then study a related model elliptic problem and propose a finite element method with a regular mesh with respect to the intrinsic metric associated with the degenerate operator. For the error estimate, we need to prove an approximation result.<\/p>","DOI":"10.1090\/s0025-5718-04-01714-4","type":"journal-article","created":{"date-parts":[[2005,4,12]],"date-time":"2005-04-12T12:20:25Z","timestamp":1113308425000},"page":"1291-1322","source":"Crossref","is-referenced-by-count":7,"title":["A partial differential equation connected to option pricing with stochastic volatility: Regularity results and discretization"],"prefix":"10.1090","volume":"74","author":[{"given":"Yves","family":"Achdou","sequence":"first","affiliation":[]},{"given":"Bruno","family":"Franchi","sequence":"additional","affiliation":[]},{"given":"Nicoletta","family":"Tchou","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2004,10,5]]},"reference":[{"issue":"3","key":"1","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1051\/m2an:2002018","article-title":"Variational analysis for the Black and Scholes equation with stochastic volatility","volume":"36","author":"Achdou, Yves","year":"2002","journal-title":"M2AN Math. 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