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Stochastic Finance, 4th Edition by Alexander Schied, Hans Föllmer

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7Superhedging

The idea of superhedging is to find a self-financing trading strategy with minimal initial investment which covers any possible future obligation resulting from the sale of a contingent claim. If the contingent claim is not attainable, the proof of the existence of such a superhedging strategy requires new techniques, and in particular a new uniform version of the Doob decomposition. We will develop this theory for general American contingent claims. In doing so, we will also obtain new results for European contingent claims. In the first three sections of this chapter, we assume that our market model is arbitrage-free or, equivalently, that the set of equivalent martingale measures satisfies

In the final Section 7.4, we discuss ...

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