Explicit characterization and backward construction of superhedging prices with transaction costs
By Amal Omrani
Appears in collection : COSA : Interactions in applied mathematics for economics, finance and Insurance / Interactions en mathématiques appliquées à l'économie, la finance et l'assurance
Under proportional transaction costs, the super-hedging price is classically a supremum over consistent price systems — complete in theory, but rarely computable.
We make it explicit in discrete time by replacing the conditional law of returns with their conditional support: the worst-case constraint reduces to a supremum over a calibrated return band, attained by convexity at its two endpoints.
This yields a closed-form one-step price — the larger of a pure-price bound and a strategy-driven bound — and the exact interval of feasible strategies. On a payoff class stable under this step, a single backward recursion reconstructs prices and hedges, finite precisely under Absence of Immediate Profit. Illustrated out-of-sample on SPY.
