Guaranteed Deterministic Approach to Superhedging: Most Unfavorable Scenarios of Market Behavior and the Moment Problem.

We consider a guaranteed deterministic problem setting of discrete-time superreplication: the aim of hedging of a contingent claim is to ensure the coverage of possible payout under the option contract for all admissible scenarios. These scenarios are given by means of a priori given compact sets that depend on the prehistory of prices: the increments of the price at each moment of time must lie in the corresponding compact sets. The absence of transaction costs is assumed. The game-theoretic interpretation implies that the corresponding Bellman–Isaacs equations hold both for pure and mixed strategies. In the present paper, we propose a two-step method for solving the Bellman equation arising in the case of a (game) equilibrium. In particular, the most unfavorable strategies of the "market" can be found in the class of distributions concentrated at most at points, where is the number of risky assets. [ABSTRACT FROM AUTHOR]