2010-08-25Buch DOI: 10.18452/8411
Convex duality in stochastic programming and mathematical finance
This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given ﬁltration. The framework uniﬁes many well-known duality frameworks from operations research and mathematical ﬁnance. The uniﬁcation allows the extension of some useful techniquesfrom these two ﬁelds to a much wider class of problems. In particular, combining certain ﬁnite-dimensional techniques from convex analysis with measure theoretic techniques from mathematical ﬁnance, we are able to close the duality gap in some situations where traditional topological arguments fail.
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