Properties of Distortion Risk Measures

@article{Balbs2008PropertiesOD,
  title={Properties of Distortion Risk Measures},
  author={Alejandro Balb{\'a}s and Jos{\'e} Garrido and Silvia Mayoral},
  journal={Methodology and Computing in Applied Probability},
  year={2008},
  volume={11},
  pages={385-399}
}
The current literature does not reach a consensus on which risk measures should be used in practice. Our objective is to give at least a partial solution to this problem. We study properties that a risk measure must satisfy to avoid inadequate portfolio selections. The properties that we propose for risk measures can help avoid the problems observed with popular measures, like Value at Risk (VaRα) or Conditional VaRα (CVaRα). This leads to the definition of two new families: complete and… 

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References

SHOWING 1-10 OF 32 REFERENCES

Coherent Distortion Risk Measures - A Pitfall

Some simulation-based testing indicates that most well-known concave distortion risk measures for sums of random couples with given marginals frequently do preserve the order of the correlations.

Coherent Measures of Risk

In this paper we study both market risks and nonmarket risks, without complete markets assumption, and discuss methods of measurement of these risks. We present and justify a set of four desirable

A Unified Approach to Generate Risk Measures

The paper derives many existing risk measures and premium principles by minimizing a Markov bound for the tail probability. Our approach involves two exogenous functions v(S) and φ(S, π) and another

Can a Coherent Risk Measure Be Too Subadditive?

It is found that for an explicitly specified confidence level, the Value-at-Risk satisfies the regulator's condition and is the most efficient capital requirement in the sense that it minimizes some reasonable cost function.

Generalized deviations in risk analysis

Connections are shown with coherent risk measures in the sense of Artzner, Delbaen, Eber and Heath, when those are applied to the difference between a random variable and its expectation, instead of to the random variable itself.

On a relationship between distorted and spectral risk measures

We study the relationship between two widely used risk measures, spectral measures and distortion risk measures. In both cases, the risk measure can be thought of as a re-weighting of some initial

Portfolio Optimization with Spectral Measures of Risk

The minimization problem of a spectral measure is shown to be equivalent to the minimization of a suitable function which contains additional parameters, but displays analytical properties which allow for efficient minimization procedures.

A CLASS OF DISTORTION OPERATORS FOR PRICING FINANCIAL AND INSURANCE RISKS

This article introduces a class of distortion operators, ga(t) = D[44-(u) + a], where D is the standard normal cumulative distribution. For any loss (or asset) variable X with a probability

A RISK MEASURE THAT GOES BEYOND COHERENCE

There are more to a risk-measure than being coherent. Both the popular VaR and the coherent Tail-VaR ignore useful information in a large part of the loss distribution; As a result they lack