Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Teemu Pennanen

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

teemu.pennanen@kcl.ac.uk

Ari-Pekka Perkkiö

Dept. of Mathematics, Technische Universität, Straße des 17. Juni 136, 10623 Berlin, Germany

perkkioe@math.tu-berlin.de

Keywords

  • Stochastic optimization
  • convex duality
  • optimality conditions

Mathematics Subject Classification

46A20, 52A41, 90C15, 90C46

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Suggested citation

S. Biagini, T. Pennanen, A.-P. Perkkiö. “Duality and Optimality Conditions in Stochastic Optimization and Mathematical Finance.” Journal of Convex Analysis 25 (2018), No. 2, 403–420. https://doi.org/10.68381/jca25028

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Published by Heldermann Verlag, 2018. Rights now held by Banach Press.