Modify Example 10.10 by changing the confidence level to $70 %$ (that is, with $h=30 %$ ).

(a) Find the conditional value at risk for $X_{1}$ of the example.

(b) Describe the family $\mathcal{P}$ of probability distributions that characterize this risk measure.

Transcribed Image Text:

Example 10.10 (CVaR characterization) Let us see how in a specific case the coherent measure CVaR can be represented as in the theorem. Consider a situation where there are five states of the world, each with a probability of .2. We wish to determine the CVaR for any X defined on the five states. For example, suppose we wish to compute p(X) = CVaR 40% (X) for various X's. As a particular case, take 10 5 X = 3. -4 -9 The average loss of the 40% worst cases is CVaR40% (X1). (With this choice of h and the given probabilities, there will be no need to split atoms.) For the given X1, VaR = -3,