Abstract
The article examines various formulations of the problem of partial hedging of American claims in an arbitrage-free and incomplete market. Market behavior scenarios are modeled by a finite tree without self-intersections. The problems are considered from the seller's viewpoint without information about buyer behavior. The main emphasis is on simplifying the constraints entering the explicit form of the buyer strategy. We find that in all problems the assumption of completely uncertain stopping time can be replaced with simpler restrictions.
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