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Our main result is a necessary and sufficient condition on the uniqueness of classical solutions to the valuation equation: the value function is the unique nonnegative classical solution to the valuation equation among functions with at most linear growth if and only if the asset price is a martingale.<\/jats:p>","DOI":"10.1137\/110842302","type":"journal-article","created":{"date-parts":[[2012,4,17]],"date-time":"2012-04-17T18:24:15Z","timestamp":1334687055000},"page":"351-373","source":"Crossref","is-referenced-by-count":17,"title":["Valuation Equations for Stochastic Volatility Models"],"prefix":"10.1137","volume":"3","author":[{"given":"Erhan","family":"Bayraktar","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Constantinos","family":"Kardaras","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Xing","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,4,17]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/s00030-007-6009-9"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-006-0011-7"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"K. Bahlali, B. Mezerdi, and Y. Ouknine,\n                      Pathwise uniqueness and approximation of solutions of stochastic differential equations\n                      , in S\u00e9minaire de Probabilit\u00e9s, XXXII, Lecture Notes in Math. 1686, Springer, Berlin, 1998, pp. 166\u2013187.","DOI":"10.1007\/BFb0101757"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1080\/17442509708834099"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-10-10306-2"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2000.6724"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"A. S. Cherny and H.J. 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