Time consistency for scalar multivariate risk measures

Time consistency of dynamic risk measures

In this paper we discuss time consistency of risk averse multistage stochastic programming problems. We show, in a framework of finite scenario trees, that composition of law invariant coherent risk measures can be law invariant only for the expectation or max-risk measures.

Time-Consistency: from Optimization to Risk Measures

Stochastic optimal control is concerned with sequential decision-making under uncertainty. The theory of dynamic risk measures gives values to stochastic processes (costs) as time goes on and information accumulates. Both theories coin, under the same vocable of time-consistency (or dynamic-consistency), two different notions: the latter is consistency between successive evaluations of a stocha...

An Empirical Comparison of Distance Measures for Multivariate Time Series Clustering

Multivariate time series (MTS) data are ubiquitous in science and daily life, and how to measure their similarity is a core part of MTS analyzing process. Many of the research efforts in this context have focused on proposing novel similarity measures for the underlying data. However, with the countless techniques to estimate similarity between MTS, this field suffers from a lack of comparative...

Dynamic convex risk measures: time consistency, prudence, and sustainability

Dynamic risk measures: Time consistency and risk measures from BMO martingales

Time consistency is a crucial property for dynamic risk measures. Making use of the dual representation for conditional risk measures, we characterize the time consistency by a cocycle condition for the minimal penalty function. Taking advantage of this cocycle condition, we introduce a new methodology for the construction of time-consistent dynamic risk measures. Starting with BMOmartingales, ...