1
$\begingroup$

I see in pflug modeling and measuring risk book, CVaR is concave... But the other book definate cvar is convex... If assume cvar is concave, then cvar optimization problem give us a global optimal point?

$\endgroup$
0
$\begingroup$

CVaR is a convex function in the underlying portfolio (measured as for instance absolute value or profit). I won't get into proving anything so instead I am going to link the first result from Google search: https://pdfs.semanticscholar.org/a5df/128eed59668b525a743a4e7f3f0efe12f930.pdf

In fact, one of the reasons that we in general think of CVaR as a superior risk measure to VaR is the fact that CVaR is a coherent risk measure and VaR is not. Convexity needs to be satisfied in order for risk measure to be coherent.

$\endgroup$
  • $\begingroup$ Thank you for your answer. Do you study the pflug "Modeling, Measuring and Managing Risk" book? $\endgroup$ – Farzin Aug 11 at 20:01
  • 1
    $\begingroup$ Pflug prove the Cvar is concave... $\endgroup$ – Farzin Aug 11 at 20:02
  • $\begingroup$ In "portfolio optimization with copula based extention conditional value at risk" paper, author said cvar is superaddative $\endgroup$ – Farzin Aug 11 at 20:05

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.