A comparison of techniques for dynamic risk (original) (raw)

A comparison of techniques for dynamic multivariate risk measures

2013

This paper contains an overview of results for dynamic multivariate risk measures. We provide the main results of four different approaches. We will prove under which assumptions results within these approaches coincide, and how properties like primal and dual representation and time consistency in the different approaches compare to each other.

A comparison of techniques for dynamic risk measures with transaction costs

This paper contains an overview of results for dynamic risk measures in markets with transaction costs. We provide the main results of four different approaches. We will prove under which assumptions results within these approaches coincide, and how properties like primal and dual representation and time consistency in the different approaches compare to each other.

Set-Valued Dynamic Risk Measures for Processes and Vectors

2021

The relationship between set-valued risk measures for processes and vectors on the optional filtration is investigated. The equivalence of risk measures for processes and vectors and the equivalence of their penalty function formulations are provided. In contrast with scalar risk measures, this equivalence requires an augmentation of the set-valued risk measures for processes. We utilize this result to deduce a new dual representation for risk measures for processes in the set-valued framework. Finally, the equivalence of multiportfolio time consistency between set-valued risk measures for processes and vectors are provided; to accomplish this, an augmented definition for multiportfolio time consistency of set-valued risk measures for processes is proposed.

Some proposals about multivariate risk measurement

Working Papers, 2008

In actuarial literature the properties of risk measures or insurance premium principles have been extensively studied. In our work we propose a characterization of some particular classes of multivariate and bivariate risk measures. Given two random variables we can ...