Time consistency of nonconvex risk measures

Although most of the theory development concerning risk measures has concentrated on convex or even coherent risk measures, nonconvex risk measures are used in practice, the prime example of course being Value-at-Risk. The purpose of this paper is to investigate the relations between various notions of time consistency for nonconvex risk measures. We focus on three notions in particular which, as we show, all satisfy a certain compatibility property that other notions of consistency do not always have.One of these notions is the strong consistency (also called dynamic consistency) that has received most attention in the literature. Despite the fact that the other two notions are weaker, we show that they are still strong enough to make consistent updates uniqueif they exist at all. We give a number of su±cient and necessary conditions that an aggregate risk measure has to satisfy for consistent updating to be possible.

Netspar, Network for Studies on Pensions, Aging and Retirement, is a thinktank and knowledge network. Netspar is dedicated to promoting a wider understanding of the economic and social implications of pensions, aging and retirement in the Netherlands and Europe.

MORE ABOUT NETSPAR


Mission en strategy           •           Network           •           Organisation           •          Magazine
Board Brief            •            Actionplan 2019-2023           •           Researchagenda

ABOUT NETSPAR

Our partners

B20160708_dnb
svb
B20211216_shell download
B20160708_uva
B20200924_Ortec Finance logo 250px_banner_small
View all partners