Geodesic
The Cheapest Superstrategy without Optional Decomposition
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Stochastic financial mathematics, Tome 237 (2002), pp. 249-255.

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We follow very closely the Föllmer and Kabanov Lagrange multiplier approach to superstrategies in perfect incomplete markets, except that we provide a very simple proof of the existence of a minimizing multiplier in the case of a European option under the assumption that the discounted process of the underlying is an $L^{2}(P)$-martingale for some probability $P$. Even if it gives the existence of a superstrategy associated with the supremum of the expectations under equivalent martingale measures, our result is much weaker than the optional decomposition theorem. 
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C. Martini. The Cheapest Superstrategy without Optional Decomposition. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Stochastic financial mathematics, Tome 237 (2002), pp. 249-255. http://geodesic.mathdoc.fr/item/TM_2002_237_a14/

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