2004/10/21 by Patrick Cheridito, Cheridito, Patrick, Freddy Delbaen +3
Decision Sciences · Economics, Econometrics and Finance · #60G35 #91B16 #91B30 #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Probability (math.PR) #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.math/0410453
openalex publication_date 2004/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study time-consistency questions for processes of monetary risk measures that depend on bounded discrete-time processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a process of monetary risk measures time-consistent if it assigns to a process of financial values the same risk irrespective of whether it is calculated directly or in two steps backwards in time, and we show how this property manifests itself in the corresponding process of acceptance sets. For processes of coherent and convex monetary risk measures admitting a robust representation with sigma-additive linear functionals, we give necessary and sufficient conditions for time-consistency in terms of the representing functionals.