HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH ⁄

摘要: We derive a formula for the minimal initial wealth needed to hedge an arbitrary contingent claim in continuous-time model with proportional transaction costs; expression obtained can be interpreted as supremum of expected discounted values claim, over all (pairs of) probability measures under which \wealth process" is supermartingale. Next, we prove existence optimal solution portfolio optimization problem maximizing utility from terminal same model; also characterize this via transformation hedging problem: one that hedges inverse marginal evaluated at shadow state-price density solving corresponding dual problem, if such exists. then use pricing claims market. The mathematical tools are those martingales, convex analysis, functional analysis and duality theory.