Before revision:  A key result in this generalization is an extension of a well known result of Ansel and Stricker in 1 . Additionally, and motivated by the works of F\"ollmer and Kramkov in 13 and Delbaen and Schachermayer in 9 , we study the hedging problem in these models and connect it to a properly defined property of "maximality" of contingent claims.
After revision:  A key result in this generalization is an extension of a well known result of Ansel and Stricker in 1 . Additionally, and motivated by the works of F\"ollmer and Kramkov in 13 and Delbaen and Schachermayer in  , we study the hedging problem in these models and connect it to a properly defined property of "maximality" of contingent claims.