{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T20:28:31Z","timestamp":1792787311425,"version":"4.5.0"},"reference-count":25,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"name":"F\u00e9d\u00e9ration Fran\u00e7aise Bancaire","award":["ANR 11-LABX-0019"],"award-info":[{"award-number":["ANR 11-LABX-0019"]}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>In this paper we propose a new methodology for solving an uncertain stochastic Markovian control problem in discrete time. We call the proposed methodology the adaptive robust control. We demonstrate that the uncertain control problem under consideration can be solved in terms of the associated adaptive robust Bellman equation. The success of our approach is to a great extent owed to the recursive methodology for construction of relevant confidence regions. We illustrate our methodology by considering an optimal portfolio allocation problem, and we compare the results obtained using the adaptive robust control method with some other existing methods.<\/jats:p>","DOI":"10.1137\/17m1137917","type":"journal-article","created":{"date-parts":[[2019,3,14]],"date-time":"2019-03-14T11:43:46Z","timestamp":1552563826000},"page":"925-946","source":"Crossref","is-referenced-by-count":26,"title":["Adaptive Robust Control under Model Uncertainty"],"prefix":"10.1137","volume":"57","author":[{"given":"Tomasz R.","family":"Bielecki","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tao","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Igor","family":"Cialenco","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Areski","family":"Cousin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Monique","family":"Jeanblanc","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,3,14]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1162\/154247603322256774"},{"key":"atypb2","unstructured":"T. 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Shreve,\n                      Stochastic Optimal Control: The Discrete-Time Case\n                      , Academic Press, New York, 1978."},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1109\/MCS.2012.2205478"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1214\/17-EJS1362"},{"key":"atypb8","first-page":"125","author":"Bordigoni G.","year":"2007","journal-title":"Berlin"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/hhi019"},{"key":"atypb10","doi-asserted-by":"crossref","unstructured":"H. F. Chen and L. Guo,\n                      Identification and Stochastic Adaptive Control\n                      , Systems Control Found. 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Knight,\n                      Risk, Uncertainty, and Profit\n                      , Houghton Mifflin Company, New York, 1921."},{"key":"atypb19","doi-asserted-by":"crossref","unstructured":"J. K\u00f6hn,\n                      Uncertainty in Economics. A New Approach\n                      , Springer, Berlin, 2017.","DOI":"10.1007\/978-3-319-55351-1"},{"key":"atypb20","doi-asserted-by":"crossref","unstructured":"P. R. Kumar and P. Varaiya,\n                      Stochastic Systems: Estimation, Identification and Adaptive Control\n                      , Classics Appl. Math. 75, SIAM, Philadelphia, 2015.","DOI":"10.1137\/1.9781611974263"},{"key":"atypb21","first-page":"66","author":"Lim A. E. 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