Equivalence between time consistency and nested formula

Henri Gérard (), Michel Lara () and Jean-Philippe Chancelier ()
Additional contact information
Henri Gérard: Université Paris-Est, CERMICS (ENPC)
Michel Lara: Université Paris-Est, CERMICS (ENPC)
Jean-Philippe Chancelier: Université Paris-Est, CERMICS (ENPC)

Annals of Operations Research, 2020, vol. 292, issue 2, No 4, 627-647

Abstract: Abstract Figure out a situation where, at the beginning of every week, one has to rank every pair of stochastic processes starting from that week up to the horizon. Suppose that two processes are equal at the beginning of the week. The ranking procedure is time consistent if the ranking does not change between this week and the next one. In this paper, we propose a minimalist definition of time consistency (TC) between two (assessment) mappings. With very few assumptions, we are able to prove an equivalence between time consistency and a nested formula (NF) between the two mappings. Thus, in a sense, two assessments are consistent if and only if one is factored into the other. We review the literature and observe that the various definitions of TC (or of NF) are special cases of ours, as they always include additional assumptions. By stripping off these additional assumptions, we present an overview of the literature where the specific contributions of authors are enlightened. Moreover, we present two classes of mappings, translation invariant mappings and Fenchel–Moreau conjugates, that display time consistency under suitable assumptions.

Keywords: Dynamic risk measure; Time consistency; Nested formula (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10479-019-03276-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:292:y:2020:i:2:d:10.1007_s10479-019-03276-1

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-019-03276-1

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().