Geodesic
Representation of Convex Operators and their Static and Dynamic Sandwich Extensions
Journal of convex analysis, Tome 24 (2017) no. 4, pp. 1375-1405
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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 Lp, 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.
Classification : 46A20, 47N30, 91B25, 91B70, 52A41
Mots-clés : Convex operator, sandwich preserving extension, dual representation, time consistency, dynamic risk measures, price operator 
@article{JCA_2017_24_4_JCA_2017_24_4_a16,
     author = {J. Bion-Nadal and G. Di Nunno},
     title = {Representation of {Convex} {Operators} and their {Static} and {Dynamic} {Sandwich} {Extensions}},
     journal = {Journal of convex analysis},
     pages = {1375--1405},
     year = {2017},
     volume = {24},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_4_JCA_2017_24_4_a16/}
}
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J. Bion-Nadal; G. Di Nunno. Representation of Convex Operators and their Static and Dynamic Sandwich Extensions. Journal of convex analysis, Tome 24 (2017) no. 4, pp. 1375-1405. http://geodesic.mathdoc.fr/item/JCA_2017_24_4_JCA_2017_24_4_a16/