Minimax theorems for American options without time-consistency. Belomestny, D., Hübner, T., Krätschmer, V., & Nolte, S. Finance Stoch., 23(1):209–238, 2019.  
Paper  doi  bibtex   @article {MR3898405,
    AUTHOR = {Belomestny, Denis and H\"{u}bner, Tobias and Kr\"{a}tschmer, Volker
              and Nolte, Sascha},
     TITLE = {Minimax theorems for {A}merican options without
              time-consistency},
   JOURNAL = {Finance Stoch.},
  FJOURNAL = {Finance and Stochastics},
    VOLUME = {23},
      YEAR = {2019},
    NUMBER = {1},
     PAGES = {209--238},
      ISSN = {0949-2984},
   MRCLASS = {91G20 (60G17 60G40 90C47)},
  MRNUMBER = {3898405},
       DOI = {10.1007/s00780-018-0378-2},
       URL = {https://doi.org/10.1007/s00780-018-0378-2},
} 
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