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Convex duality in stochastic programming and mathematical finance

Teemu Pennanen (teemu.pennanen***at***tkk.fi)

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.

Keywords: Convex duality, stochastic programming, mathematical finance

Category 1: Stochastic Programming

Category 2: Applications -- OR and Management Sciences (Finance and Economics )

Category 3: Convex and Nonsmooth Optimization


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Entry Submitted: 09/16/2010
Entry Accepted: 09/16/2010
Entry Last Modified: 05/04/2011

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