Multivariate coherent risk measures induced by multivariate convex risk measures

Positivity ◽  
2019 ◽  
Vol 24 (3) ◽  
pp. 711-727
Author(s):  
Yanhong Chen ◽  
Yijun Hu
Keyword(s):  
Risk Measures ◽  
Coherent Risk Measures ◽  
Convex Risk Measures ◽  
Coherent Risk

scholarly journals Teoria de Medidas de Risco: uma revisão abrangente

2014 ◽  
Vol 12 (3) ◽  
pp. 411
Author(s):  
Marcelo Brutti Righi ◽  
Paulo Sergio Ceretta
Keyword(s):  
Risk Management ◽  
Literature Review ◽  
Value At Risk ◽  
Risk Measures ◽  
Fundamental Aspect ◽  
Coherent Risk Measures ◽  
Convex Risk Measures ◽  
Coherent Risk ◽  
Comprehensive Literature Review ◽  
Generalized Deviation

A fundamental aspect of proper risk management is the measurement, especially forecasting of risk measures. Measures such as variance, volatility and Value at Risk had been considered valid because of their practical intuition. However, a solid theoretical framework it is important to ensure better properties for risk measures. Such background is the risk measures theory. This paper presents a comprehensive literature review on risk measures theory, focusing in basic theory and extensions to this fundamental outline. The paper is structured in order to cover the main risk measures classes from literature, which are coherent risk measures, convex risk measures, spectral and distortion risk measures and generalized deviation measures.

REPRESENTATION OF BSDE-BASED DYNAMIC RISK MEASURES AND DYNAMIC CAPITAL ALLOCATIONS

2014 ◽  
Vol 17 (05) ◽  
pp. 1450032 ◽  
Author(s):  
EDUARD KROMER ◽  
LUDGER OVERBECK
Keyword(s):  
Risk Measures ◽  
Risk Measure ◽  
Static Case ◽  
Coherent Risk Measures ◽  
Dynamic Risk Measures ◽  
Convex Risk Measures ◽  
Coherent Risk ◽  
Dynamic Risk ◽  
Entropic Risk Measure ◽  
Representation Result

In this paper, we provide a new representation result for dynamic capital allocations and dynamic convex risk measures that are based on backward stochastic differential equations (BSDEs). We derive this representation from a classical differentiability result for BSDEs and the full allocation property of the Aumann–Shapley allocation. The representation covers BSDE-based dynamic convex and dynamic coherent risk measures. The results are applied to derive a representation for the dynamic entropic risk measure. Our results are also applicable in a specific way to the static case, where we are able to derive a new representation result for static convex risk measures that are Gâteaux-differentiable.

scholarly journals Restricted Coherent Risk Measures and Actuarial Solvency

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Christos E. Kountzakis
Keyword(s):  
Minimization Problem ◽  
Risk Measures ◽  
Insurance Company ◽  
Coherent Risk Measures ◽  
Dual Representation ◽  
Coherent Risk ◽  
Representation Form ◽  
Solvency Capital

We prove a general dual representation form for restricted coherent risk measures, and we apply it to a minimization problem of the required solvency capital for an insurance company.

scholarly journals Rearrangement Invariant, Coherent Risk Measures on L<sup>0</sup>

2015 ◽  
Vol 04 (01) ◽  
pp. 22-25
Author(s):  
Christos E. Kountzakis ◽  
Dimitrios G. Konstantinides
Keyword(s):  
Risk Measures ◽  
Coherent Risk Measures ◽  
Coherent Risk
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