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Journal of Convex Analysis 25 (2018), No. 2, 403--420
Copyright Heldermann Verlag 2018

Duality and Optimality Conditions in Stochastic Optimization and Mathematical Finance

Sara Biagini
LUISS G. Carli, Viale Romania 32, 00197 Roma, Italy

Teemu Pennanen
Dept. of Mathematics, Strand Building, King's College London, London WC2R 2LS, England

Ari-Pekka Perkkiö
Dept. of Mathematics, Technische Universität, Straße des 17. Juni 136, 10623 Berlin, Germany

This article studies convex duality in stochastic optimization over finite discrete-time. The first part of the paper gives general conditions that yield explicit expressions for the dual objective in many applications in operations research and mathematical finance. The second part derives optimality conditions by combining general saddle-point conditions from convex duality with the dual representations obtained in the first part of the paper. Several applications to stochastic optimization and mathematical finance are given.

Keywords: Stochastic optimization, convex duality, optimality conditions.

MSC: 46A20, 52A41, 90C15, 90C46

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