Conditional Value at Risk (CVaR) Model by GAMS

[Syed Ali]

Dear Gams Friend.

If there is anybody here who models Conditional value at Risk Models by GAMS.

My confusion is on definition of  conditional value at Risk. My confusion is given below-

I want to minimize worst case cost and write CVaR as
CVaR =A+(1/1-B) *Sum(s,P(s)*V(s)),

where , A=VaR;
B= confidence level .
Now when I solve the model using B=0.99 or 0.95 or 0.90, I ger VaR=CVaR which is not acceptable. also we get same tail cost  for every scenario after solving the model if we such values of B.

When I use B=0.01 or 0.05 or 0.1 then ,  I get CVaR is greater than VaR that is acceptable and the solution is reasonable.

My question is regarding B. If I write the CVaR equation like above, what should the value of B? In particular, whether 1-B=99% for example Or 1-B=1%.

Please help me clarify on this.

Regards,
Syed

[Mehrdad Tahmasebi]

Daer Syed Ali,

Can write simple example of your objective? 

Regards

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[Syed Ali]

Thanks for your reply.  I again run the model. I observed that upto confidence level 0.70, The CVaR is greater than VaR. for a confidence level greater than 0.70
CVaR equals VaR.

In theory, we see that CVaR is greater than equal to VaR. Depending on the model and data, may be CVaR equals VaR at some point. I hope, you might interpret the situation better. 
I have provided an example of my model.

Regards,
Syed

[Juliana]

Dear Syed

Im facing a similar problem did you find a solution to this issue ?

Regards 

[Syed Ali]

Dear Juliana,

Technically, VaR = CVaR when B is greater than 0.861. This is because the number of samples(scenarios) are few, so we need much more samples.

Here's one more thing.

As you probably know,

V(s) >= f(s)-A.

f(s) = total cost in scenario "s."
.

Regards,

Syed

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Have fine.
Warm Regards,
Syed Mithun Ali, Assistant Professor, Department of Industrial and Production Engineering, Bangladesh University of Engineering and Technology. Dhaka-1000, Bangladesh.
Mobile no: +8801916034096/+8801718370993
Alternative email: mit...@ipe.buet.ac.bd
http://www.buet.ac.bd/ipe/faculty1.html