Model-independent Superhedging under Portfolio Constraints
AbstractIn a discrete-time market, we study the problem of model-independent superhedging of exotic options under portfolio constraints. The superhedging portfolio consists of static positions in liquidly traded vanilla options, and a dynamic trading strategy, subject to certain constraints, on the risky asset. By the theory of Monge-Kantorovich optimal transport, we establish a superhedging duality, which admits a natural connection to convex risk measures. With the aid of this duality, we derive a model-independent version of the fundamental theorem of asset pricing under portfolio constraints. It is worth noting that our method covers a large class of Delta constraints as well as Gamma constraint.
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Date of creation: Feb 2014
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