Minimax estimation of value-at-risk under hedging of an American contingent claim in a discrete financial market

The game problems between seller and buyer of an American contingent claim relate to large scale problems because a number of buyer's strategies grows overexponentially. Therefore, decomposition of such games turns out to be a fundamental problem. In this paper we prove the existence of a minimax monotonous (in time) strategy of the seller in a loss minimization problem considering value-at-risk measure of loss. The given result allows to substantially decrease a number of constraints in the original problem and lets us turn to an equivalent mixed integer problem with admissible dimension.