# Questions tagged [coherent-risk-measure]

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### Proof for expected shortfall sub additivity

I found on pag 5 https://faculty.washington.edu/ezivot/econ589/acertasc.pdf the proof about the sub additivity of expected shortfall. I understood the demonstration on the whole, but I would like to ...
49 views

### Showing that VaR is not sub additive

I found on pag 2 and 3 of Martin Haugh's Risk Measures, Risk Aggregation and Capital Allocation, 2010 (in this file http://www.columbia.edu/~mh2078/RiskMeasures.pdf ) an example showing non sub ...
1 vote
38 views

### How to use coherent risk measure for evaluating price?

Coherent risk measures are defined by number of axioms (see e.g. Coherent Risk Measure) but a question that does not seem well studied is how to use them. Let's take a coherent risk measure $\rho$ and ...
1 vote
129 views

### Industry or academic standard frequency to report the return, standard deviation, and Sharpe ratio?

Everyone (funds, banks, academics, financial information sites etc.) reports the annualized return, standard deviation, and Sharpe ratio. Yet we never get to know what the basis of their computation ...
273 views

### Expected Shortfall monotonicity

I have to show monotonicity for a more general case than the expected shortfall. I have to show that $E(X|X \geq a) \geq E(X|X \geq b), \forall a,b \in \mathbb{R}$ so that $a\geq b$ and $F_X(a-)<1$....
121 views

### Chorent risk measure with superaddative

In some definition of chorent risk measure Superadditive is one of the properties I don't understand Why? With subadditivity and homogeneous CvaR is convex, but if we assume another definition for ...
60 views

### Choquet integral risk measure

I have one question that cannot fully understand why. What is the definition of the Choquet integral risk measure?
90 views

### Bregman Mean of a Distribution

In a paper (link), author writes, given that $\gamma:R\rightarrow \bar{R}$ is a convex function, $dom_{\gamma}:=\{x\in R:\gamma(x)<+\infty\}$ is a non-empty open set and $\gamma$ a closed proper ...
1 vote
72 views

### Risk Measure-identication

Let X be a variable with existing moment generating function $M_x(z)=E[e^{zX}]$. Define the following risk measure: $\rho_{\alpha}(X)=inf_{z>0}(z^{-1}ln(\frac{M_x(z)}{1-\alpha}))$ Does anyone know ...
83 views

### Example of Coherent Risk measure with Compact Representation

Every coherent risk measure $\rho$ can be represented as $$\rho(X)\triangleq \sup_{Q \in \mathcal{Q}} \mathbb{E}\left[ -X \right],$$ for a set of probability measures $\mathcal{Q}$ defined on the ...
467 views

### What are the advantages of $EVaR$ over $CVaR$?

$CVaR$, which is short for Conditional Value-at-Risk, has long been accepted by both academe and practice as a good coherent risk measure. Entropic value-at-risk ($EVaR$) is a comparative new coherent ...
1k views

### Calculating Expected Shortfall of combined portfolios

So I am reading lecture notes here: https://courses.edx.org/c4x/DelftX/TW3421x/asset/Week3_var_3_slides.pdf The example is this: We have two independent portfolios of bonds. They both have a ...
356 views

### How to calculate the distortion function for CVaR?

Can anyone give me some hints as to how to prove that $$g(x) = \begin{cases} \frac{x}{1-\alpha}, &0 \leq x \leq 1-\alpha\\ 1 , &1-\alpha \leq x \leq 1 \end{cases}$$ ...
1 vote