Abstract
We reduce the computation of price bounds of contingent claims to a sequence of interconnected finite dimensional optimization problems, depending on a parameter. In a perfect market model the obtained formulas characterize upper hedging price, while in a multicurrency market model with transaction costs they describe the set of initial portfolios, allowing for superhedging of a vector contingent claim. The mentioned formulas do not contain martingale measures or their analogues. The proofs are based on the martingale selection theorem. The effectiveness of the proposed approach is illustrated by several examples.
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