Abstract

Monotone convex operators and time-consistent systems of operators appear naturally in stochastic optimisation and mathematical finance in the context of pricing and risk measurement. We study the dual representation of a monotone convex operator when its domain is defined on a subspace of LpL_p, with 1 ≤ p ≤ ∞, and we prove a sandwich preserving extension theorem. These results are then applied to study systems of such operators defined only on subspaces. We propose various dynamic sandwich preserving extension results depending on the nature of time: finite discrete, countable discrete, and continuous. Of particular notice is the fact that the extensions obtained are time-consistent.

Author information

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

Giulia Di Nunno

Dept. of Mathematics, University of Oslo, P. O. Box 1053 Blindern, 0316 Oslo, Norway
and: NHH Norwegian School of Economics, Helleveien 30, 5045 Bergen, Norway

giulian@math.uio.no

Keywords

  • Convex operator
  • sandwich preserving extension
  • dual representation
  • time consistency
  • dynamic risk measures
  • price operator

Mathematics Subject Classification

46A20, 47N30, 91B25, 91B70, 52A41

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Suggested citation

J. Bion-Nadal, G. Di Nunno. “Representation of Convex Operators and their Static and Dynamic Sandwich Extensions.” Journal of Convex Analysis 24 (2017), No. 4, 1375–1405. https://doi.org/10.68381/jca24079

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Published by Heldermann Verlag, 2017. Rights now held by Banach Press LLC.