Representation of convex operators and their static and dynamic sandwich extensions

2014/12/05 by Jocelyne Bion–Nadal, Jocelyne Bion-Nadal, Bion-Nadal, Jocelyne +2
Computer Science · Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.FA #math.PR

paper · pdf · doi:10.48550/arxiv.1412.2030

33 pages

openalex publication_date 2014/12/05 · arxiv created 2016/05/31 · arxiv updated 2016/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Monotone convex operators and time-consistent systems of operators appear naturally in stochastic optimization 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 L_p, with p∈ [1,∞], 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.

Related

• Monotone Operator Theory in Convex Optimization
• A Nonlinear Sandwich Theorem
• Valuations and dynamic convex risk measures
• Linear Monotone Subspaces of Locally Convex Spaces
• Limits of maximal monotone operators driven by their representative functions