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Under a wide class of two-sided L\u00e9vy models with a general random refraction time, we rigorously show that the optimal strategy to exercise successive call options is uniquely characterized by a sequence of upcrossing times. The corresponding optimal thresholds are determined explicitly in the single stopping case and recursively in the multiple stopping case.<\/jats:p>","DOI":"10.1137\/140957317","type":"journal-article","created":{"date-parts":[[2015,8,11]],"date-time":"2015-08-11T11:28:27Z","timestamp":1439292507000},"page":"2373-2405","source":"Crossref","is-referenced-by-count":5,"title":["Optimal Multiple Stopping with Negative Discount Rate and Random Refraction Times under L\u00e9vy Models"],"prefix":"10.1137","volume":"53","author":[{"given":"Tim","family":"Leung","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kazutoshi","family":"Yamazaki","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongzhong","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,8,11]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1214\/105051605000000377"},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"S. 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