Convex Duality in Stochastic Optimization and Mathematical Finance

Authors:
Teemu Pennanen
Affiliations:
Department of Mathematics and Statistics, University of Jyväskylä, FI-40014 Jyväskylä, Finland
Venue:
Mathematics of Operations Research
Year:
2011

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Abstract

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 techniques from 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.