{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T03:18:57Z","timestamp":1787368737337,"version":"build-2736575974"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2013,1]]},"abstract":"<jats:p>We show that the value function of a stochastic control problem is the unique solution of the associated Hamilton--Jacobi--Bellman equation, completely avoiding the proof of the so-called dynamic programming principle (DPP). Using the stochastic Perron's method we construct a supersolution lying below the value function and a subsolution dominating it. A comparison argument easily closes the proof. The program has the precise meaning of verification for viscosity solutions, obtaining the DPP as a conclusion. It also immediately follows that the weak and strong formulations of the stochastic control problem have the same value. Using this method we also capture the possible face-lifting phenomenon in a straightforward manner.<\/jats:p>","DOI":"10.1137\/12090352x","type":"journal-article","created":{"date-parts":[[2013,11,7]],"date-time":"2013-11-07T12:03:33Z","timestamp":1383825813000},"page":"4274-4294","source":"Crossref","is-referenced-by-count":52,"title":["Stochastic Perron's Method for Hamilton--Jacobi--Bellman Equations"],"prefix":"10.1137","volume":"51","author":[{"given":"Erhan","family":"Bayraktar","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mihai","family":"S\u00eerbu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2013,11,7]]},"reference":[{"key":"atypb1","unstructured":"E. Bayraktar and M. S\u00eerbu,<i>Stochastic Perron's method and verification without smoothness using viscosity comparison: Obstacle problems and Dynkin games<\/i> Proc. Amer. Math. Soc., to appear."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-2012-11336-X"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/090752328"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/11.1.59"},{"key":"atypb5","unstructured":"J. Claisse, D. Talay, and X. Tan,<i>A Note on Solutions to Controlled Martingale Problems and Their Conditioning<\/i> preprint, http:\/\/www.cmapx.polytechnique.fr\/$\\sim$tan\/JDX.pdf (2013)."},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1992-00266-5"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1032374469"},{"key":"atypb8","unstructured":"J. Diehl, P. K. Friz, and H. 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