A guaranteed deterministic approach to superhedging: mixed strategies and game equilibrium

Abstract

For a discrete-time superreplication problem, a guaranteed deterministic formulation is considered: the problem is to ensure a cheapest coverage of the contingent claim on an option under all scenarios which are set using a priori defined compacts, depending on the price history: price increments at each moment of time must lie in the corresponding compacts. The market is considered with trading constraints and without transaction costs. The statement of the problem is game-theoretic in nature and leads directly to the Bellman - Isaacs equations. In this article, we introduce a mixed extension of the ``market'' pure strategies. Several results concerning game equilibrium are obtained.