Summary: For the discrete-time superreplication problem, a guaranteed deterministic formulation is proposed: the problem is to ensure the cheapest coverage of the contingent claim on an American option under all admissible scenarios. These scenarios are set by a priori defined compacts depending on the price history; the price increment at each moment of time must lie in the corresponding compact. The market is considered without trading constraints and transaction costs. The problem statement is game-theoretic in nature and leads directly to the Bellman-Isaacs equations of a special form under the assumption of no trading constraints. In the present study, we estimate the modulus of continuity of uniformly continuous solutions, including the Lipschitz case.
For the entire collection see [Zbl 1425.91013].